Announcing appearances, publications, and occasional thoughts on natural philosophy and ancient history by philosopher, historian, and author Richard Carrier.

Richard Carrier is the renowned author of several books including Sense and Goodness without God and Proving History, as well as numerous articles online and in print. His avid readers span the world from Hong Kong to Poland. With a Ph.D. in ancient history from Columbia University, he specializes in the modern philosophy of naturalism and humanism, the origins of Christianity, and the intellectual history of Greece and Rome, with particular expertise in ancient philosophy, science and technology. He has also become a noted defender of scientific and moral realism, Bayesian reasoning, and the epistemology of history. For more about him and his work visit www.richardcarrier.info.

EVENTS

Ex Nihilo Onus Merdae Fit

A common argument against atheism is that the Big Bang proves everything had a beginning (it does not in fact prove that, but bear with me here), therefore there was once nothing, and ex nihilo nihil fit, “from nothing, comes nothing.” However, that latter premise is demonstrably false. And that spells death for theism and marvelous glory for atheism. And I don’t even mean in the Lawrence Krauss A Universe from Nothing sense, since he doesn’t actually mean “nothing” when he talks about nothing (a point I’ll get back to in a moment). No, I mean, even granting the theist’s premise that if there was no God, then there was once absolutely nothing, and therefore there cannot have been a universe, therefore the fact that we are here entails God exists, because our existence would be literally impossible otherwise. I am saying that even granting that premise, all those “therefores” don’t actually follow. They are complete non sequiturs. In fact, I am not just saying that; I’m even saying that the exact opposite is true, that when we grant that premise (the theist’s own premise!), then a whole shitload of stuff will necessarily exist. Huwah? Yeah. And not a pejorative load of shit. An actual shitload.

I’ve been asked to explain this so many times lately (going all the way back to Mike Licona in our second debate) that I’ve decided to blog it so I can just point people here (that’s kind of the reason for everything I write, really).

I am an empiricist, which means I don’t truck with a priori reasoning. But there is one good use for the latter: to deduce from a hypothesis what would be the case if that hypothesis were true (and what the case if it were false); because then you can go look and see what you observe and thus determine how likely it is that that hypothesis is true (or false). This is the basic foundation of scientific method, the “hypothetico-deductive method” (which in Proving History I demonstrate is fundamentally Bayesian, but I won’t go on about that here). This is not actually a priori, because you still have to go looking around, and your conclusion is never absolutely certain but always some matter of probability. So here I am not saying there ever was nothing. There might well have always been something. Or quite a lot of things really. The argument that that is impossible, owing to confusions about infinite sets, is also bogus, and based on fundamental ignorance of logic and mathematics (as I’ve explained before).

So I am not actually conceding the premise that there was once absolutely nothing. I’m just analyzing that as a hypothesis, to see what it entails if it were true. So here goes…

Which ‘Nothing’ Is That Again?

First we must define “absolutely nothing.” There are actually many different kinds of nothing (John Barrow even wrote a book about it: The Book of Nothing). Krauss, for example, means by “nothing” a collapsed region of space-time governed by certain laws of quantum physics. But that’s not actually nothing. For one thing, you have space-time. That’s something. And you have “certain laws of quantum physics” (a minimal set of which he describes, and which, if it always existed, he shows would entail that a universe would arise spontaneously very much like ours, no God needed; which conclusion was also reached and demonstrated by Stephen Hawking in The Grand Design, and likewise by Victor Stenger in God: The Failed Hypothesis, pp. 132-33, with extensive support in The Fallacy of Fine Tuning and The Comprehensible Cosmos). That’s also something. Quite a few things, really. Now, Stenger has made a case (in The Comprehensible Cosmos) that those “few things” are in fact logically necessary if we presume no God exists (and thus no agency exists to decide the world should be one way rather than another); for example, if no agency exists to entail an objective reference frame or to alter the outcomes of random events, then the whole of Relativity Theory is logically entailed by default, and likewise all the laws of thermodynamics. It’s an interesting argument, but not one I will assume as proven here.

Really, my only task at present is to define what we must mean by absolutely nothing. This can only mean that nothing whatever exists except anything whose non-existence is logically impossible. That latter caveat is unavoidable for the obvious reason that if it is logically impossible for something not to exist, then there can’t have ever been a state of being where it did not exist. So if by “absolutely nothing” you mean even the non-existence of logically necessary things, then “absolutely nothing” is logically impossible, and thus there can’t ever have been “nothing” in that sense. So if that’s what theists mean by “if there was no God, then there was once absolutely nothing,” that not even logically necessary things existed, then their claim is self-refuting. We can then dismiss it out of hand. But if they allow that logically necessary things still exist even when there is otherwise nothing, then we have a “nothing exists” that is logically possible. There could have been such a state of being, of there once being nothing, in that sense.

Of course, theists will then want to introduce their ontological arguments at this point, which purport to prove that God is one of those things whose existence is logically necessary, but no such argument ever succeeds. They are all invalid or unsound (the clearest demonstration of this is to be found in Malcolm Murray’s most excellent desk reference for atheists, The Atheist’s Primer, pp. 55-73). And one could in principle pull a Victor Stenger here instead, and aim to prove that certain basic laws of physics are logically necessary. And such a task might even succeed.

But I’m not depending on any such proposal here. All I will assume is what is undeniably true: that all the fundamental propositions of logic and mathematics are necessarily true (for example, all valid and sound theorems and syllogisms are necessarily true, in the sense that, when given their premises, their conclusions cannot be false; but not in the sense that their premises are necessarily true, even if they might be), and therefore there can never have been a state of being in which they were false. For example, it can never have been the case that “if you form a polygon from only straight lines, on a flat plane, with only three sides, then the sum of the angles produced within that polygon will not equal 180 degrees.” More importantly, it can never have been the case that the basic laws of probability were false (such as complementarity, unity, and exclusivity), nor can the basic laws of logic have ever been false (as that would be logically impossible by definition; that is, to say that the laws of logic are false, is by definition to say that logically impossible things can exist, and therefore logically necessary things can in that case not exist after all…so much for God!).

One might object at this point by asking how the laws of logic can “exist” when nothing exists. There are two ways to answer that, one is to refer to the naturalist ontology of logic, whereby things like numbers and laws describe what always potentially exists, even when nothing actually exists (see my book Sense and Goodness without God III.5, pp. 119-34, esp. III.5.4-5, pp. 124-34), and when nothing actually exists, all potentials exist (because then nothing actually exists to prevent anything from potentially existing, which point I’ll revisit in a moment). But another is to simply refer back to the simple point that if the laws of logic don’t exist, then by definition that means logically impossible things can exist. Which is fine if you really want to entertain that as a hypothesis. Good luck with that (I don’t think you’ll get very far: Sense and Goodness without God II.2.2.7, pp. 42-43, and III.9.3, pp. 188-91). Meanwhile, I will simply take it as granted by all sane parties that logically impossible things can’t exist. Certainly, that is a premise most theists must accept. At least, if you can really get them to deny it, then you’ve pretty much gotten them to publicly confess to being crazy. And one hardly need continue arguing with a confessed lunatic.

Now, when nothing exists (except that which is logically necessary), then anything can happen (whose happening is logically possible). Because the only way to prevent something from happening, is to have some law or force or power or object or agency, in other words some actual thing, that prevents it. If you remove all obstacles, you allow all possibilities. This is a logically necessary truth. The only thing that is prevented, is the logically impossible. Because, as we have concluded so far, even when “nothing” exists, all logically necessary truths still exist. And here “exist” means only in the sense of being true; obviously the laws of logic aren’t made of aluminum-titanium alloy with a mass of twelve earths and located precisely one light year below galactic south; it is a fallacious prejudice to assume “existence” requires mass, substance, or discrete location, although perhaps it does require something.

For instance, I have argued that that which exists at no location or at no point in time, by definition exists never and nowhere, which is by definition not existing. So one might think that if nothing exists, no place or time exists, therefore logical truths cannot exist. However, since it is logically impossible for logical truths not to exist, if logical truths must exist at some point in spacetime, then it would follow that spacetime is logically necessary and therefore there can be no “absolute nothing” that lacks at least a singular point of spacetime (which is of course practically nothing). Thus logical necessity can prevent things from happening. But if that’s all there is, then everything else can happen, because nothing exists to prevent it.

And So the Baby Goes Out with the Bathwater…

This is why ex nihilo nihil fit is necessarily false. For that is a law. And a law is not nothing. A law is something. To say that “from nothing comes only nothing” is to say that some law of physics (like, say, the law of conservation of energy) exists to prevent nothing from generating anything else except more nothing. But if nothing exists, then that law of physics doesn’t exist. Since it is not logically necessary that nothing can only produce nothing, then when nothing exists except what is logically necessary, the law ex nihilo nihil fit doesn’t exist either. Therefore, that “absolute nothing” that once existed will not have been governed by such a law. It cannot have been. Because if it were, it would then not be nothing, but the inexplicable and arbitrary existence of something: a weird law of physics with no origin or agency. Thus it is a logical contradiction to say “there once was absolutely nothing, and that absolute nothing can only have produced nothing.”

From here on out it only gets worse for the theist. Not only will there have been nothing to prevent anything from happening, there won’t have been anything to make any one thing more likely than any other. For example, quantum mechanics entails that some things are more likely than other things; if whatever the fundamental structure is that causes quantum mechanics to work didn’t exist, then some things would not be more likely than other things. Everything would be as likely as anything else. Because the only way to make one thing more likely than something else, is for something to exist that makes the one thing more likely than the other. In some cases, logical necessity can do that. But not in every case. The number of universes that exist, for example. There is no logical necessity for there to be only one universe. Or any other specific number of them. And if nothing exists to decide how many there will be, all possible outcomes are equally likely. There being just one universe will be just as likely as there being seven of them, or a million of them, or any other number of them. And if we count all configurations, then smaller numbers actually become lessprobable than larger ones (as I’ll demonstrate shortly).

Getting Everything from Nothing

I draw out the consequences of this fact in The End of Christianity (ch. 12, “Neither Life Nor the Universe Appear Intelligently Designed,” note 20, pp. 408-09). I quote the relevant material here:

In our background knowledge b we have no knowledge of any law of physics that would prevent there being other universes (and no means of seeing if there are none), so the probability that there are is exactly what that probability would be if the number of universes that exist were selected at random. Of all the possible conditions that could obtain (no universe; just one universe; two universes; three; four; etc., all the way to infinitely many universes), that there would be only one universe is only one out of infinitely many alternatives. This entails it is effectively 100 percent certain an infinite multiverse exists because the probability of there being only one universe is then 1/INFINITY, which is [approximately] 0 percent. In fact, for any finite number n of universes, the probability of having only that many or less is n/INFINITY, which is still [approximately] 0 percent. If the probability of having any finite number of universes is always [approximately] 0 percent, then the probability that there is an infinite multiverse is [approximately] 100 percent. This further entails we have no need to explain why there is something rather than nothing: as then nothing (a state of exactly zero universes) also has a probability of 1/INFINITY, which is again [approximately] 0 percent. The probability that there will be something rather than nothing is therefore [approximately] 100 percent. This conclusion can only be averted if something were proved to exist that would change any of these probabilities, thereby making nothing (or only one thing) more likely than any other logical possibility. But we know of no such thing. Therefore, so far as we must conclude given what we actually know, there is an infinite multiverse, and there must necessarily be an infinite multiverse (both to a certainty of [approximately] 100 percent).

This is an epistemological argument (it does not claim to prove there is an infinite multiverse, but only that so far as we know there is; some future knowledge might change that conclusion). But if we grant the metaphysical premise “there was once absolutely nothing,” then this epistemological argument becomes a metaphysical argument: it is then logically necessarily the case that there is an infinite multiverse.

Therefore, if we grant the theist’s premise, that there was once absolutely nothing (no spacetime, no God, and no laws of physics, beyond those that may be logically necessary), it necessarily follows that there is an infinite multiverse (or to be more precise, the probability that there wouldn’t be is infinitely near to zero). From a simple demonstration of probability, it then follows that the universe we find ourselves in will also necessarily exist (or again to be precise, the probability that a universe essentially like ours wouldn’t exist is infinitely near to zero). Therefore, the theist’s own premise entails a godless universe will exist that looks exactly (in all relevant particulars) like the one we find ourselves in. Ooops.

Proving It

The formalization of the argument proceeds as follows:

P1: In the beginning, there was absolutely nothing.–

P2: If there was absolutely nothing, then (apart from logical necessity) nothing existed to prevent anything from happening or to make any one thing happening more likely than any other thing.–

C1: Therefore, in the beginning, nothing existed to prevent anything from happening or to make any one thing happening more likely than any other thing.–

P3: Of all the logically possible things that can happen when nothing exists to prevent them from happening, continuing to be nothing is one thing, one universe popping into existence is another thing, two universes popping into existence is yet another thing, and so on all the way to infinitely many universes popping into existence, and likewise for every cardinality of infinity, and every configuration of universes.–

C2: Therefore [given logical necessity], continuing to be nothing was no more likely than one universe popping into existence, which was no more likely than two universes popping into existence, which was no more likely than infinitely many universes popping into existence, which was no more likely than any other particular number or cardinality of universes popping into existence.–

P4: If each outcome (0 universes, 1 universe, 2 universes, etc. all the way to aleph-0 universes, aleph-1 universes, etc. [note that there is more than one infinity in this sequence]) is no more likely than the next, then the probability of any finite number of universes (including zero universes) or less having popped into existence is infinitely close to zero, and the probability of some infinite number of universes having popped into existence is infinitely close to one hundred percent.–

C3: Therefore, the probability of some infinite number of universes having popped into existence is infinitely close to one hundred percent.–

P5: If there are infinitely many universes, and our universe has a nonzero probability of existing (as by existing it proves it does, via cogito ergo sum), then the probability that our universe would exist is infinitely close to one hundred percent (because any nonzero probability approaches one hundred percent as the number of selections approaches infinity, via the infinite monkey theorem, similar to the law of large numbers).–

C4: Therefore, if in the beginning there was absolutely nothing, then the probability that our universe would exist is infinitely close to one hundred percent.

I’ve already shown that P1, once granted, entails P2. And P4 and P5 are logically necessary truths (they can only be false if the basic laws of logic and probability are false, which, as I said, is by definition logically impossible). And C1-4 are all logically necessary if P1-5 are true (given the following connotation of P3). So that leaves P3. There are two objections sometimes raised against it. The first is that it is incomplete; the second is that its demarcation of possibilities is arbitrary or contrary to set theory. [Another objection, that infinite probability distributions are impossible, is simply false.]

As to the first objection, (1) there are presumably things that can pop into existence besides universes; and (2) there are many different kinds of universes possible, so each number of universes would represent an infinitely divided fraction of possible combinations of that many universes.

As for (2), that makes no difference to the argument. As long as nothing existed to make any particular universe more likely than any other (and given P1 and P2, nothing did), then C2 as stated remains true on P3. For example, “zero universes” would be infinitely less probable than one universe if we counted each of infinitely many singular universes as being equally likely as any other outcome, but if that’s the case, then zero universes remains no more probable than one universe, as C2 states; and in consequence, P4 also remains true as stated. And likewise for every number of universes above that. Such considerations are therefore irrelevant.

As to (1), if we define “universe” as “any collection of actually existing things (whether it consists of just one thing or several) that is completely separated from other collections or in some way connected to other collections but entails a fundamentally different physics from them,” then P3 remains true, and so on down the line. Because then by definition nothing else can pop into existence but some universe or other. What then distinguishes one universe from another (thereby making two universes, instead of just one universe consisting of two combined collections) is a fundamental separation or a fundamental difference in its governing physics. In the latter case those universes won’t be physically separated, but in the unity of them both, one physics will govern one region and another physics will govern the other, making for two universes, even if, for instance, they are both just different parts of one combined region of spacetime. [You could still count this binary universe as one universe, but then you would have to count its twin as one universe, i.e. a universe otherwise identical but in which the relative positions of each distinguished region are swapped in the same space-time manifold, so you still get two universes, each as likely as the other.]

This leads to the second objection: that this demarcation is improper. Isn’t one “metaverse” with two different regions of governing physics more complex than one single universe with only one governing physics, and therefore isn’t the former much less probable than the latter? Actually, no. Because we are selecting at random from the set of all possible states of being. For example, one binary metaverse will be one state of being, while a singular universe will be another state of being. Therefore the probability of selecting one or the other is equal, because in each case there is only one possibility that can manifest, and the sum of those possibilities is two. And in fact, once we start counting configurations, the odds go in the other direction. Think of a bag of infinite marbles, inside each of which is a possible outcome (a number and configuration of universes). Will it be more likely that you will draw a “one universe” marble than a “two universe” marble? To the contrary, there are far more possible configurations of two universes, so in fact there are far more “two universe” marbles in that bag than “one universe” marbles. Therefore, choosing a “one universe” outcome is not more probable than choosing a “two universe” outcome (in fact it is on this reasoning a great deal less probable). Thus, P3 as stated remains true and (in conjunction with C1) entails C2 as stated.

Therefore C2 remains true, therefore C3 remains true, and there must then be an infinite multiverse, if in the beginning there existed absolutely nothing. And that means C4 remains true, and our universe, in effect, necessarily exists. This leaves the theist in a bind. If we start with their assumption that (if there was no God) there was once absolutely nothing, then we get our universe, no God needed. There can be no doubt that “absolutely nothing” is a vastly simpler entity than any God (much less their preferred God, who just happens to have all these convenient powers and properties, and not only that, but just happens to have them in infinite degree, which has to be the luckiest existential dice roll conceivable). So if a vastly simpler hypothesis explains all the evidence, we must prefer it (because it is necessarily vastly more probable: see Proving History, pp. 81, 104-06). In other words, Occam’s Razor slits God’s throat right good.

Winning the Whac-a-Mole Twostep

But maybe P1 is false. Certainly, the theist must retreat to insisting it is, now that we’ve just proven P1 explains the universe better than his God does. Well, then something has always existed (or just existed in the beginning for no reason, either way). They say it is God. We would say it is something decidedly ungodlike; namely, a very basic physics. In other words, the basic physical assumptions of Krauss, Hawking, or Stenger. Or anyone else. It doesn’t matter. As I’ve explained before, we don’t need to know which originating physics began it all, to know it’s far more probable that some such thing did than that a god did (upon request I even postulated ten different possibilities, all of which having a greater prior probability than a God). For Krauss, Hawking, and Stenger, it’s a simple quantum vacuum (whose properties are much more basic than God’s, and every single one of which has been scientifically proven to exist, unlike any of the unique properties of God, much less his existence), from which they can deduce the universe we observe. In fact, as I prove in The End of Christianity (ch. 12, “Neither Life Nor the Universe Appear Intelligently Designed”), the scientific evidence conclusively fits the deductive predictions of that hypothesis, in precisely the way it doesn’t fit the deductive predictions of any plausible God. So if something always existed for no reason, and our options are that this something was either God or a simple quantum vacuum, the evidence confirms it was the latter. And if that’s the case, then quantum vacuum it is.

Oh, and I’d also like your authorization to translate your post into Spanish and Italian and use it as discussion material in some of my lectures, with due credit. Of course, I would send you the translations for you to use it in any way you like.

piero:Oh, and I’d also like your authorization to translate your post into Spanish and Italian and use it as discussion material in some of my lectures, with due credit. Of course, I would send you the translations for you to use it in any way you like.

Yes, you have my permission to do that, with full attribution. I don’t need a copy. But if you post it online, feel free to post the URL here.

On a related note, I have seen TImothy McCabe attempt to prove that something cannot come from nothing. He argues that something coming from nothing would be like 0 plus 0 equaling one, which is a necessarily false statement. On the other hand, our universe is said by physicists (Hawking and Krauss in the books you mentioned) to contain equal amounts of positive and negative energy, in which case our universe coming from nothing would be like saying 0 equals 1 and (-1), which is true!

Lastly, if it is impossible for something to come from nothing, and God cannot do that which is logically impossible, it follows that it is impossible for God to create something from nothing. So the point theists try to prove inevitably ends up torpedoing their own argument!

Ryan:There is one worry that I have about this argument: It applies probability (finite) to an infinite range (the sum of all possible universes, which is infinite).

Even if we don’t have a completed transfinite probability theory (although we might, see below), we can already infer some conclusions that would be entailed by it. This can be proven graphically, for example. Imagine a dart board on which resides every natural whole number, and every cardinality of infinity (in other words, every logically possible quantity), such that each shares the same area as the other (this is basic calculus, the summation of infinitesimals, accomplished even by Archimedes). Throw a dart at it, such that it will land at random on the board. What is the probability that it will strike a finite number? Almost the whole area of the board will be occupied by cardinalities of infinity. The answer is therefore obvious. It gets trickier when you start comparing domains of cardinalities and asking the probability of landing in that domain. But even if we lacked a mathematical tool to answer that question, that in no way negates the fact that we can answer the previous question.

I have seen Timothy McCabe attempt to prove that something cannot come from nothing. He argues that something coming from nothing would be like 0 plus 0 equaling one, which is a necessarily false statement.

The analogy doesn’t apply, because zero is something (a discrete quantity), not nothing (or rather, not absolutely nothing). Likewise addition is something (an act of combination), not nothing. 0+0=1 is a statement in which the terms are all defined, and thus is necessarily true by virtue of those definitions. By the same process, my argument proceeds, not his, i.e. once we define our terms (P1), my conclusion follows. His does not.

On the other hand, our universe is said by physicists (Hawking and Krauss in the books you mentioned) to contain equal amounts of positive and negative energy, in which case our universe coming from nothing would be like saying 0 equals 1 and (-1), which is true!

I issue caution in making much of this. There is a fundamental logical flaw in their argument. They are saying that the energy of mass is equal to the energy of gravity; but mass causes gravity, and is measured in terms of it, so that they should be equal is logically necessary, wholly regardless of any need to balance “positive” with “negative” energy, which terms are semantically meaningless in this context anyway, since gravity is very definitely positive energy (that’s why water wheels produce power, rather than drain it). Even in the Standard Model, gravity is just another force mediated by particles called gravitons which have an Einsteinian mass. It therefore actually makes no sense to talk about gravity as “negative” energy, or as “canceling out” all other energy.

Lastly, if it is impossible for something to come from nothing, and God cannot do that which is logically impossible, it follows that it is impossible for God to create something from nothing. So the point theists try to prove inevitably ends up torpedoing their own argument!

Unfortunately that doesn’t work, because God is not nothing. Thus, something would not be coming from nothing in that scenario; it would be coming from God.

I don’t know, I’d say zero is simply a representation of an absence. If there are 0 particles and 0 dimensions of spacetime and 0 of everything else, we could call that nothing.

“Unfortunately that doesn’t work, because God is not nothing. Thus, something would not be coming from nothing in that scenario; it would be coming from God.”

But God can’t create matter *from* himself, he’d have to create ex nihilo, from nothing. And if it is impossible for matter to come from an absence of matter, then it is impossible for God to do it. A theist could go for idealism (The Universe is not an actual physical place, it’s just a dream God is having) but then that wouldn’t explain why we need a heart and lungs to live, as John Loftus pointed out in The End of Christianity.

Ryan:I don’t know, I’d say zero is simply a representation of an absence. If there are 0 particles and 0 dimensions of spacetime and 0 of everything else, we could call that nothing.

But notice what you are doing. You had to add things to zero (“particles, dimensions, everything else”). If you said “0 particles” that would not be nothing, because something could exist other than particles. Etc. If you have to add “everything” then you are no longer saying “0” you are saying “0 anything,” and when you say that, the laws of arithmetic no longer produce 0{anything}+0{anything}=0{anything}, precisely because that statement assumes a stable reality, i.e. that there is something that keeps a 0 a 0. Which my argument proves is false.

Another way to put it is this: 0{anything}=0{laws governing what will or won’t exist}; and 0{laws governing what will or won’t exist}+0{laws governing what will or won’t exist} /= 0{anything}; to the contrary, 0{laws governing what will or won’t exist}+0{laws governing what will or won’t exist} = {infinitely many things}, as my argument proves. It’s akin to infinities not obeying common sense (because finite arithmetic no longer applies): when you define a quantity at 0 that includes things that keep a 0 a 0, you have just defined away the very thing that keeps a 0 a 0.

And if it is impossible for matter to come from an absence of matter, then it is impossible for God to do it.

Yes, if that were a law of physics that always governed nothingness, and if god could not violate it for some reason, then God could not create. But that’s a lot of ifs.

In fact, if “it is impossible for matter to come from an absence of matter,” then there would not be God + nothing, but instead God + (that law of physics + nothing). The latter combination is not nothing. It’s something. In other words, where did that law of physics come from? It didn’t come from God. It didn’t come from nothing. It isn’t logically necessary. So why would it exist?

First, let me just say I love your writing and am really looking forward to reading your books whenever I get the chance. (Consider this my confession as a bad heathen that I haven’t already done so. However, I have seen you speak, and you’re every bit as hilarious in person as you are in writing.)

This is an interesting argument, but I’m somewhat confused. Maybe you could elaborate a little further on it?

P2: If there was absolutely nothing, then (apart from logical necessity) nothing existed to prevent anything from happening or to make any one thing happening more likely than any other thing.

I don’t understand how you get to the idea that something can happen if nothing exists. Is it logically necessary that something can happen, and if so, why? I guess that’s a weird question, because we obviously do know “things can happen” given the universe’s existence, but if we remove all of that and only deal with the logically necessary, then I don’t see why that must be. Sure, nothing is there to prevent something from happening, but what would necessitate that “somethings” or “happenings” are possible?

consciousness razor:I don’t understand how you get to the idea that something can happen if nothing exists.

Because if nothing exists, then nothing exists to prevent anything from happening. As I said, if you remove all obstacles, you allow all possibilities.

This is why it’s crucial to distinguish absolutely nothing, from physical nothing (e.g. empty space). The latter is not the former. The latter imposes obstacles and thus prevents things from happening (because space is an actual thing, and has properties, including shape). Although even then, what it prevents depends on its properties: as Krauss et al. point out, we have confirmed that “empty space” actually spontaneously creates particles constantly, even as we sit here it’s doing this around and inside us; it’s just that they all cancel each other out, so the net effect looks like “nothing” to us, being that we “live” on a vast scale beyond the subatomic (though, in fact, most of your weight consists of these spontaneous particles, so really you are observing them right now, through their gravitational effects on your body).

This physical space still obeys certain rules, however, which follow from its structure (the structure of spacetime). An absolute nothing has no structure, and thus is governed by no rules. By definition. So, yes, it’s ability to spontaneously become something else is logically necessary…if “an absolute nothing” has ever existed; again, so far as I know, it is not “logically necessary” that it ever did. But that’s a separate question.

Thanks for the response. Honestly, I’m still confused, which isn’t unusual, but it’s a little bit clearer than it was yesterday. I may just need to think about it more.

Because if nothing exists, then nothing exists to prevent anything from happening. As I said, if you remove all obstacles, you allow all possibilities.

Yes. If I’m understanding correctly, you’re basically establishing that there are such possibilities, thus refuting the claim that they are impossible. And it also doesn’t follow that Jesus watches you masturbate. Great. If that’s the basic idea, then it makes sense to me.

I’ve been trying and failing to articulate the problem I’m having (if it makes any sense at all), so I’ll spare you the word salad for now. It’s probably irrelevant, because it seems you’re not attempting to explain why some shit actually exists, just that it possibly exists, which is all you need for the purposes of this argument. Right?

consciousness razor:It seems you’re not attempting to explain why some shit actually exists, just that it possibly exists, which is all you need for the purposes of this argument. Right?

Technically, all I’m doing is demonstrating what is logically entailed if P1 is true (I’m not actually defending the truth of P1). However, I do think the fact that P1 explains so much so well, with so little, that it’s a pretty good candidate for being true. Much more so than any god. And in that sense, it would explain “why some shit actually exists” (simply put: some shit actually exists, because the probability that nothing would exist is infinitely close to zero).

Hi Richard,
I’m so glad you and Ophelia Benson are part of the same blogging network. It’s through regularly checking Ophelia’s blog, and clicking through to FTB that I’m encountered your blog amongst others. I’d heard your name before, but not read much of your work.
On the strength of this post, I bought ‘Sense and Goodness without God’ on Kindle. Unfortunately, it means, I haven’t finished ‘Not the impossible faith. I hope your future books are on Kindle too.
Regarding the logic of this article. I’ll need to go over it again. But I like it. It appears that, given that a believer would argue that their God is logical (why would they try to use reason if it weren’t, let along be able to conceptualize it) then all else falls into place as logic is given. Brilliant!
But I can’t claim to have fully understood it yet….
Anyway, keep blogging. I really like you historical posts too.

Brian: Thanks for the kind words. Yes, I have made sure all my books are available on kindle, and I will aim to make sure all future ones will be as well (although the release date for kindle versions can be months after the print version sometimes).

Oh, and I didn’t know that merda was gold or silver age latin. I thought it was more modern, say dark ages or medieval and hence: merde (French), merda (Italian), mierda (Spanish). I imagined in Latin it was just faeces….Perhaps that’s your point. Ex nihilo onus nihil fit is church latin or similar?

Brian: Even in imperial Latin, faex or fex (pl. faeces or feces) meant dregs or lees, as of wine; by extension “foul,” but not in the sense of shit, but in the sense of dregs or dirty water. Merda was always the word for shit. Oh, and onus is not in the original formula. I added that. It means “load,” hence onus merdae, “shitload.”

I’m having some trouble with P4: it seems to me that P4 can be false if the likelihoods of the individual outcomes are simply incomparable: neither more than, less than, nor equal to each other. More precisely, it’s not clear to me that “the likelihood of there being 0 universes, given that there was initially nothing” is a well-defined quantity, at least without more premises than you supply here. A related objection (or possibly another way of stating the same objection) is that taking about there “continuing to be nothing” or a universe “popping into existence” (to say nothing of talking about “the beginning” in the first place) seems to presuppose the existence of time, and it’s not clear to me that time is logically necessary.

Geoff Romer:it seems to me that P4 can be false if the likelihoods of the individual outcomes are simply incomparable: neither more than, less than, nor equal to each other.

That’s a logical impossibility. Since every outcome is possible, and per P2 equally possible, it cannot be the case that any outcome is “neither more than, less than, nor equal” to any other outcome. Since all logical necessities by definition necessarily exist (even when nothing else exists), then P4 is necessarily true.

More precisely, it’s not clear to me that “the likelihood of there being 0 universes, given that there was initially nothing” is a well-defined quantity, at least without more premises than you supply here.

The only hidden premises are all logically necessary truths (like the above), which shouldn’t have to be stated.

A related objection (or possibly another way of stating the same objection) is that taking about there “continuing to be nothing” or a universe “popping into existence” (to say nothing of talking about “the beginning” in the first place) seems to presuppose the existence of time, and it’s not clear to me that time is logically necessary.

No time is presupposed, because the decision is instantaneous. Indeed, it is existential, i.e. in the absence of anything to entail what will exist, anything can exist. Therefore, what will exist is C3. This would be true even if time didn’t exist (e.g. even if time were logically impossible and only static timeless universes could exist).

What we usually mean by time is among the things that will pop into existence, i.e. some of the universes that come to exist will exhibit a time dimension; and, incidentally, many won’t, thus many timeless static universes will exist.

But, semantically, you can say a static timeless universe does have at least one dimensionless point of time (that of simply existing), but if we define time that way, then the existence of time is logically necessary, and therefore it would be logically impossible for time not to exist, and therefore time (in this sense) must exist even in a state of nothing (I already made that point in the blog, e.g. if logically necessary things must exist at some time, because they cannot “never exist” and if they cannot never exist, it is necessarily the case that they exist at some time, therefore time necessarily exists, but only in this most reductive sense in which anything timeless necessarily exists “in” a single dimensionless point of time).

P2 doesn’t say they’re “equally possible” (by which I assume you mean equally probable). To infer that they are equally probable, you need an additional premise (call it P2.1) that the probabilities of any two things are equal, in the absence of something to make them different.

Consider, for example, P2*: If there was absolutely nothing, then (apart from logical necessity) nothing existed to make any one thing greener than any other thing. In order to conclude that all things are equally green, I need the additional P2.1*: Any two things are equally green, in the absence of something to make them different.

Obviously I can (and should) deny P2.1* on the grounds that it is not logically necessary for all things to have an attribute of greenness. To establish P2.1 you have to, at a minimum, demonstrate that it is logically necessary for all possible things to have an actual probability, and to do that you’d have to define probability in a way that still makes sense when nothing exists. It’s not at all clear to me how you’d do that.

Geoff Romer:[Re: “Since every outcome is possible, and per P2 equally possible…”] P2 doesn’t say they’re “equally possible” (by which I assume you mean equally probable). To infer that they are equally probable, you need an additional premise (call it P2.1) that the probabilities of any two things are equal, in the absence of something to make them different.

P2 states “If there was absolutely nothing, then…nothing existed to prevent anything from happening or to make any one thing happening more likely than any other thing.” That latter part entails all outcomes are equally possible (the statements are synonymous). So P2 does say that.

(Mathematically: {x /> y /> x} = {x = y}; the two statements are identical in meaning)
If there was absolutely nothing, then (apart from logical necessity) nothing existed to make any one thing greener than any other thing. In order to conclude that all things are equally green, I need the additional P2.1*: Any two things are equally green, in the absence of something to make them different…Obviously I can (and should) deny P2.1* on the grounds that it is not logically necessary for all things to have an attribute of greenness.

Your analogy doesn’t hold, because P1 entails all possibilities, whereas the domain of green things does not consist of all possibilities. Therefore it’s obvious that P2.1* is false because, as you say, there are possible things other than green things. But there are no possible things other than all possible things. So P2 is true. It cannot be rebutted by saying there are some possible things that are not in the set of all possible things.

You’d have to define probability in a way that still makes sense when nothing exists.

I did that when I argued that probability theory is necessarily true, all necessary truths necessarily exists, therefore, the truths of probability theory exist when nothing exists (otherwise we would have a logically impossible state: a state in which logically necessary truths were not true).

Because of this, P1 logically entails P2 (as I showed). And P2 is the proposition “that it is logically necessary for all possible things to have an actual probability” (Because if any possible thing does not have an actual probability, then it is impossible; therefore, any possibility that is not impossible must have an actual probability; if P1, then everything is not impossible that is not logically impossible; ergo, every possibility has an actual probability; in other words, if A then B; ~B; therefore ~A; a proper denial of the consequent, or modus tollens.)

P.S. Another way to construe the same objection (not that I’m attributing it to anyone here; it was suggested offlist) is that given P2 it does not follow that every possibility will be equally probable, because perhaps the probability of each thing will be selected at random. This, however, requires a special additional randomizer, which is a thing, and therefore cannot exist if nothing exists. Only a logically necessary randomizer can exist on P1 (such as the logical necessity of some possibility being selected from all available possibilities, i.e.the sum of probabilities for all possibilities is 100%, therefore the probability of some one possibility being selected is 100%, and therefore a logically necessary truth).

In the absence of all things, including some extra thing that can randomly assign every possibility to a probability, each possible thing is as probable as every other. In short, as worded, P2 states that no thing exists “to make any one thing happening more likely than any other thing.” A randomizer that made some things more likely than other things (even if for no reason) is a thing that makes one thing happening more likely than another thing. Therefore P2 already states that no such randomizer exists. And that is correct: since such a thing is not logically necessary, it does not exist on P1. To the contrary, on P1 nothing exists “to make any one thing happening more likely than any other thing,” including unnecessary randomizing powers. Therefore C2 follows.

I think the issue of time does reveal a possible contradiction in the argument, though.

You postulate the state that nothing exists, and then derive the state that infinite universes must exist.

Without time, we cannot move from one state to another state, and the two states are in clear contradiction.

I would argue that without time, then all events are logically impossible (as events are points in spacetime), including anything popping into existence, therefore there is in fact a logical reason preventing the spontaneous generation of universes even in a state of pure nothingness.

I think the issue of time does reveal a possible contradiction in the argument, though. You postulate the state that nothing exists, and then derive the state that infinite universes must exist. Without time, we cannot move from one state to another state, and the two states are in clear contradiction.

You are presupposing rules that don’t exist when nothing exists. That is therefore no longer nothing. The question is not whether nothing causes something in time, but whether nothing will cause there to be time. When absolutely nothing exists, a timeline can spontaneously replace it, because that is then among the things that can happen. In other words, of all the things that are possible “moving from one state to another” is one of those things, which thing would itself simultaneously entail time (i.e. the spontaneous transition would itself create time, it is not “time first, then something” but “something, including time, immediately exists”).

That’s why “meta-time” is not needed if there are no rules governing what will happen.

We can also existentially ask “what is the probability that nothing and only nothing will exist?” and get the same result (that probability is effectively zero) even if the universe is past eternal (i.e. even if there was never a state of nothing). But even supposing a past state of nothing, there is no logical contradiction produced if time pops out of it. Because the change of state and the materialization of time are simultaneous. We do not need time to appear first, then a change of state. If there is a change of state, there automatically is time. (See my previous comments on this, in each case the time question is the last item discussed here and here and here.)

A better way to think of it is as a problem in non-Euclidean geometry.

Let’s assume we’re only talking about universes with two dimensions of space and one of time. These can be described as a three dimensional shapes (which will be familiar to you). At one end of which (call it the “Big Bang”) is a singular point of time on the left hand side at which everything begins (from which a volume of space expands). But it’s a static shape (say, a cone, for example), and all time exists along its axis (a world tube for the whole universe). That is one possible universe.

We can use this same process to model a nothingverse (in that case we have only the singular point of time and space and nothing else), and a somethingverse without time (a singular point of time surrounded by a plane of spatial points at which things exist statically, with no change; this could have the shape of a wheel, for example, where the plane of the wheel is the time dimension and two dimensions of space are the points along the wheel), and a somethingverse with time (this would be a solid shape, a volume, one radius of which is the time axis, the rest the two dimensions of space, each slice along the time axis being that 2D space at a different time).

Since all of these shapes are logically possible, all of these universes are logically possible. It would be illogical to point to the starting point of time, that singular point of time all the way to the left, and say no other shapes are possible because those shapes would require transitioning from that one-dimensional point, and that contradicts the fact that transitioning would require more points of time to exist first, but since they don’t, they can’t. Since we can imagine those other shapes existing (instantaneously and thus eternally), this refutes the argument. Clearly it is not logically impossible to have shapes that begin from a singular point of time but consist of more than a singular point of time.

The source of confusion may be that you are imagining a “hyper-time” inside which “sub-time” has to be created. But that’s fallacious. From a POV outside of time, no hyper-time is needed. The difference between a single point of time and an extended line of time is simply the existence of time. You don’t need “extra” time to drag that point of time into a line of time, as if there were two separate time dimensions, and one of them is created inside the other. The event of there being only one point of time or a line of time is decided instantaneously (when no rules govern what shape will exist).

Another way to think of it is that the universe does not begin at a state of nothing to the left of the first point of time. The universe begins at that first point of time. The only question is, what universe will there be? Will it be just a single point of space-time? Or one of the infinitely many other shapes possible? It is not as if there is a single point of space-time that floats around a while and then suddenly becomes another shape. It is an instantaneous physical event. If, for example, we get a volume, there will never be a single point of space-time. You can search the entire history of that universe and you will never find it. Of all the things that could happen, that wasn’t it. You will find an originating point of space-time. But that’s not the same thing. Because that point is part of a line and always has been. There was never a time when it wasn’t.

Thus, there was never a time when there was nothing. There was only a time when there was only a single point of space-time–but since no thing governed whether there would be only that or a line extending from it, then whether there will be only that or a line extending from it is decided randomly. The transition from a nothing-state to a something-state is instantaneous, and the transition itself is one of the things that could exist, and it’s probability of existing is the same as any alternative (like there being no such transition, which is just one possibility among infinitely many). The only time you need to make that transition possible is the time that the transition itself consists of, and since they appear together, simultaneously, there is no need to smuggle the time in first and then accomplish the transition. All we have to ask is, what are the odds that such a transition will not exist?

How do you reconcile this with P1, “In the beginning, there was absolutely nothing.”? On the face of it, you appear to be contradicting your premise, in which case you have proved P1 to be false by reductio ad absurdum. This in itself is a good thing to do, but rather negates your speculation that P1 may be true and so may explain our existence.

I can only assume you are making a distinction between the timeline of a child universe (within which there is no time when there is nothing) and that of the parent nothingness which spawned it (which begins with nothing).

If that is the case, you would indeed appearing to be assuming the hypertime you deny.

You’ve raised a lot of points in this comment, in others and in email correspondence. There’s a lot to deal with so I’m writing up my response as a series of blog posts which I will link to here when they are done.

Someone off list made an objection that indicated that they didn’t know about transfinite set theory, and I realized some other readers might have the same gap in their knowledge, so I thought I’d address that here.

The naive objection was (rephrased to its simplest form) “if infinity is one quantity, then the probability in P4 ‘infinitely close to 100%’ is incorrect, because that is only the probability of infinity or less; the actual probability of getting infinity is the same as getting zero universes or one universe, because, like them, infinity is just one possibility.”

This is incorrect. Infinity is not one quantity. There are in fact infinitely many infinities, each larger than the next, and they are labeled aleph-0, aleph-1, etc. (I even linked to the wikipedia page explaining this, where I mention this labeling in the original post), all the way to aleph-aleph, and then another sequence starts, and so on.

The domain of aleph-0 (the lowest cardinality of infinity) or less will have an infinitesimal probability of receiving a selection, per P4. The remaining probability space consists of all other cardinalities of infinity. Therefore the probability of selecting a quantity from among the infinite cardinalities of infinity is infinitely close to 100%, and the probability of selecting a quantity from among the finite numbers and aleph-0 (the first infinity) is infinitely close to 0%.

P.S. Last year on a backchannel a philosopher tried to argue against my thesis by insisting that any summation of infinitesimals must equal either zero or infinity, therefore no probability distribution is possible, since that requires all probabilities sum to 1 (which, as this argument goes, infinitesimals can’t do). But this is false, and is soundly refuted by all experts on infinitesimal mathematics. In the event anyone else wants to raise the same objection:

K.D. Stroyan & W.A.J. Luxemburg, Introduction to the theory of infinitesimals (Academic, 1976), p. 53: the “existence of…nonzero infinitesimals follows from Theorem (4.3.1)” [which is presented on p. 52; likewise “the reciprocal of an infinite number is infinitesimal” and “the reciprocal of a nonzero infinitesimal is infinite” and there is in fact an infinite set of infinitesimals, i.e. not all infinitesimals are equal, just as not all infinities are equal].

H. Jerome Keisler, Elementary Calculus: An Approach Using Infinitesimals (PDF), pp. 27-34 also proves the above, e.g., p. 28, “there is a hyperreal number that is greater than zero but less than every positive real number,” in other words, there is an infinitesimal that is not equal to zero. Likewise, the text there explains that an infinite sum of infinitesimals (unlike a finite sum of them), defined as a multiplication of an infinitesimal by an infinity (p. 31), can equal a nonzero finite number, depending on which infinitesimals are being summed.

Some of this can also be gleaned from the Wikipedia entry “infinitesimal.”

Summations of infinitesimals using ordinary arithmetic fail because ordinary arithmetic is not valid for transfinite quantities (i.e., that it is valid for finite quantities has been axiomatically proven with set theory; that it is valid for transfinite quantities has never been proven, and given that the propositions required to prove it for finites are false for transfinites, such a proof is unlikely).

Instead you must use hyperreal arithmetic, e.g. wherein +* is the analogous function to + (Keisler, p. 28). The “+” sum of an infinite number of infinitesimals will be either zero or infinity, but the “+*” sum of an infinite number of (some kinds of) infinitesimals will not be zero or infinity, but some finite number. Since “+” summation is invalid for infinitesimals, while “+*” summation is valid for infinitesimals, the conclusion using “+” is invalid; while the conclusion using “+*” is valid, therefore we must accept it.

Accordingly, we can have an infinite probability distribution that sums to 1. Likewise, since the reciprocal of any transfinite is some infinity (and this has been formally proven per the resources above), any quantity shown to be infinitesimal entails a reciprocal that is infinite. Therefore the converse of an infinitesimal probability is an infinite probability, which means an infinite share of the probability space, hence [approximately] 100% (strictly speaking, it is 1 – {infinitesimal}, which expression is in fact well defined and meaningful, as Keisler shows in explaining the standard part principle, pp. 35-38).

Burt Rosenberg (Probability for Algorithm Students) says “For continuous probability…events may have probability zero without being impossible, and calculus is needed to sum over these infinitesimals to get a finite number.” Thus even mathematical experts in probability agree that you can have an infinite distribution in probability theory. (Google around and you’ll find many examples of calculus being employed to determine probability densities from infinite probability distributions.)

Richard, are you planning any public debates on god in the near future? I would love to hear this argument used in a public debate against someone like william lane craig. I think you would do much better than krauss or stenger.

Thanks. Very interesting. It reminds me a little of the Yoga Vasistha, a purportedly ancient book arguing that the “world-appearance” (described like a multiverse in the book) has no real substance and actually does not exist at all, but that the appearance of a world is persistent because of nothing real existing to prevent it.

I take Richard’s argument in the following sense (if I’m wrong, he’ll no doubt correct me):

“Nothing” cannot possibly be the case, because the verb “to be” (or “to exist”) cannot coherently be applied to non-being. When I say “That house is” or “That house exists”, I’m merely saying “That house”. To say “That house” when in fact that house was not, the phrase would be incoherent. There is no semantic difference between “house big” and “the house is big”. In order to use the verb “to be” at all, we have to be able to point to the object in question.

Since “nothing”, by definition, is not, the state of nothingness is inherently incoherent, because we can not point to it. If the laws of logic apply in all possible worlds, then “nothingness” can never be the case, simply because what is not cannot be. Hence, nothingness is merely the label we attach to a non-space-time which must necessarily give rise to space-time.

Oh, no, that’s not my argument. On my argument, “nothing” can be; it just has a probability infinitely closely to zero. Your argument I think is invalid because it presumes a referring agent (someone to say things about what exists), whereas if nothing exists, no such agent exists either, and therefore the inability of an agent to point to it cannot be an objection to it (although obviously, if an agent exists to point to things, then yes, “a state of nothing” in that event does not exist, simply because an agent pointing at things is not “nothing”).

Chris Harris:One objection that I always hear to this line of argument is that “having ‘potential’ is something, thus not nothing.” That is, if you have nothing, this will include the absence of potential.

Since the lack of a potential thing entails the presence of an actual thing (the thing that blocks that potential), the absence of potential things entails the presence of actual things, which is not nothing. Therefore a state of absolutely nothing that lacked both actual things and potential things is logically impossible. So if logically impossible things can’t exist, then absolutely nothing does indeed contain all potential things (hence my point that if you want to insist that nothing means even the absence of logically necessary truths, then what you mean by “nothing” is impossible and cannot exist.)

Since the lack of a potential thing entails the presence of an actual thing (the thing that blocks that potential), the absence of potential things entails the presence of actual things, which is not nothing.

I don’t think this follows.

Potential things can not exist for two reasons. First, because there is an actual thing blocking the actualization of the potential thing, which you mentioned. Second, because if potential things depend upon actual things to exist all, then the absence of potential things could mean the absence of actual things.

Remember, there is the actual thing X with the potential to become Y, and then there is the actual thing Z, which blocks X’s becoming Y, and thus blocks X’s potential to become Y. X could not become Y either if there is a Z blocking this process, or because there simply is no such thing as X at all.

dguller:Potential things can not exist for two reasons. First, because there is an actual thing blocking the actualization of the potential thing, which you mentioned. Second, because if potential things depend upon actual things to exist all, then the absence of potential things could mean the absence of actual things.

If a potential thing could not logically exist but for some actual thing preceding it, then yes, that potential would be a logical impossibility and therefore would not exist when nothing exists. But can you prove that all possible universes are logically impossible but for some previously existing thing? (Other than logically necessary things, of course, which will preexist.) That would be amazing. I am not aware of it ever being done.

I don’t think you can do it, but do present the proof if you can.

Basically, what I predict will happen is that we can define two sets of universes, those for whom some actual thing must preexist before that universe can exist, and those for whom that is not the case. The former set will indeed not arise from nothing (they will have a probability in that case of zero). But that still leaves the latter set. Which is the actual set of all possible universes (since even the first set will only consist of universes caused to exist by universes in the second set, and therefore all the universes in the first set will exist to some probability, as parts of universes in the second set).

So you would have to prove that the second set is empty.

[Or not empty but finite, which would be an interesting thing to discover. And would entail an entirely new argument than mine. But I see no likelihood of its contents being anything but infinitely infinite. Because we can take almost any universe in the first set, take away its necessity of a preceding thing, i.e. remove that proposition from the description of that universe or transform it into a proposition of simultaneous appearance, which will leave a logically coherent and thus logically possible universe, and have a corresponding universe in the second set. Even universes in the first set which cannot have that proposition removed without contradiction, will correspond to a universe consisting of only that preexisting thing, or set of things, which will then exist in the second set, and if it materializes, will cause to exist the corresponding universe in the first set. Which means the second set will contain at least as many members as the first set.]

You seem to sometimes equivocate between the potential for X to become Y, and the actualization of the potential for X to become Y. The former exists irrespective of whether the latter actually happens, but the latter could not possibly happen without the former. They are different.

dguller:You seem to sometimes equivocate between the potential for X to become Y, and the actualization of the potential for X to become Y. The former exists irrespective of whether the latter actually happens, but the latter could not possibly happen without the former. They are different.

I see nowhere where I equivocate. What actually happens is not predetermined by any of the potentials. It is not caused to happen by anything, except logical necessity. Thus the only thing we need to exist to actualize some potential is logical necessity. Which necessarily exists, and therefore is not absent in a state of absolutely nothing.

Unless, of course, by saying “the actualization of a potential cannot happen without some actual thing” you mean everything must have a cause, in which case you are simply stating a non sequitur. In no way is it logically necessary that everything have a cause; and even insofar as there is a cause, that cause is logical necessity in this case, and thus the actuality that causes the result is present, not absent (because its absence is logically impossible).

I see nowhere where I equivocate. What actually happens is not predetermined by any of the potentials. It is not caused to happen by anything, except logical necessity. Thus the only thing we need to exist to actualize some potential is logical necessity. Which necessarily exists, and therefore is not absent in a state of absolutely nothing.

I suppose that depends upon your conception of where logic derives its force. The account that I find the most compelling is that logical necessity is an abstraction from the patterns and regularities of the real world. No patterns and regularities of the real world, then no logical necessity. If that is true, then if there is nothing, then there are no patterns or regularities, and then there is no logical necessity.

Also, how can logical necessity cause anything by itself? After all, logical necessity is a necessary relationship between propositions. If propositions must refer to states of affairs in order to have sense, then you first have states of affairs, which are referred to by propositions, which have various logical relationships between them. In that case, it would be the states of affairs and their relationships that are the causal force behind logical necessity. That would mean that if there are no states of affairs, as in absolute nothing, then there would be no logical necessity either.

Unless, of course, by saying “the actualization of a potential cannot happen without some actual thing” you mean everything must have a cause, in which case you are simply stating a non sequitur. In no way is it logically necessary that everything have a cause; and even insofar as there is a cause, that cause is logical necessity in this case, and thus the actuality that causes the result is present, not absent (because its absence is logically impossible).

First, what I meant is that you cannot have the potential without some actual being to potentially become something else. Potential is not some free-floating something, but simply represents the possible future outcomes of an actual being. For, a red ball is potentially blue. You have to have an actual ball to potentially become something else. In other words, you must first have something before it can become something else. And that doesn’t work with absolute nothing at all.

Second, since we have never come across any event without any cause, I’m not too sure why you want to go out on this limb. I don’t even know what an uncaused event would look like. After all, an uncaused event would also be an event without any reason, and thus would be incomprehensible from a rational standpoint. I don’t think it helps to build a system upon a foundation of irrational principles.

And quantum mechanics doesn’t help much here, because just because underlying causes don’t show up in the formalism does not mean that they do not exist. No more than the fact that genetics does not show up in a Bell curve of height mean that genetics is not involved in how the curve works. The map is not the terrain.

dguller:The account that I find the most compelling is that logical necessity is an abstraction from the patterns and regularities of the real world. No patterns and regularities of the real world, then no logical necessity. If that is true, then if there is nothing, then there are no patterns or regularities, and then there is no logical necessity.

That is a non sequitur. “Nothing” entails patterns and regularities–indeed, you yourself keep insisting it has the “pattern or regularity” of always staying nothing and never doing anything. That is a pattern and a regularity. You can’t escape it. Something that had no patterns or regularities would by logical necessity have the pattern and regularity of never having any pattern or regularity. Thus the complete absence of pattern or regularity is a logical impossibility. Do you see what I mean? That is what logical necessity means. You cannot have a state in which there is no pattern or regularity; because the absence of a pattern or regularity is a pattern or regularity.

Carry this through and you’ll realize the only way to have anything like the complete absence of pattern or regularity, is to have a state that obeyed no rules (other than logical necessity). My argument then proceeds. See how that works?

(As to your confusions about propositions, see my previous reply.)

First, what I meant is that you cannot have the potential without some actual being to potentially become something else. Potential is not some free-floating something, but simply represents the possible future outcomes of an actual being.

And in this context, we are talking about “the possible future outcomes of an actual being,” the “actual being” being “absolutely nothing,” which means of the only sort that is possible, which is one which possesses all logically necessary properties. One of those properties is the power to become anything else, because there are no constraints on what it will become, and the absence of constraints logically entails the power to do anything. You can only prevent “nothing” from having that property by adding “something” to it (something that isn’t logically necessary and thus has to exist for no reason), and then it’s not nothing.

For, a red ball is potentially blue. You have to have an actual ball to potentially become something else. In other words, you must first have something before it can become something else. And that doesn’t work with absolute nothing at all.

Yes, it does. Because nothing has properties, too: all logically necessary properties, in fact. And we do “first have something before it can become something else,” that “something” being this particular “nothing” (the nothing that has all logically necessary properties).

It is fallacious to say that it is “logically necessary” that a ball exists before a ball exists, for example; and it is just as fallacious to say that it is “logically necessary” that “atoms” exist before a ball exists (because even insofar as a ball must be made of atoms, they can come into existence simultaneously); and so on all the way down the line. There is, in other words, no logical contradiction in the statement “a ball came into existence without a cause.” Therefore, you cannot say we “must” have a cause (whether a ball, or prior atoms, or prior anything whatever). That is to confuse physical necessity with logical necessity. A physical necessity is created by an actuality, not the absence of it.

I don’t think it helps to build a system upon a foundation of irrational principles.

You do not have a very good idea of what an “irrational” principle is. You keep talking about what you can’t imagine as if that were what was logically impossible. Those are not the same thing, a warning I issue in some detail in my follow-up post (The God Impossible).

dguller:You seem to lean heavily upon the idea that if X is logically possible, then X eventually becomes real. I’m wondering how this can be justified.

It’s the other way around. How is “if X is logically possible, then X does NOT eventually become real” justified? That is, what’s to stop it happening? It’s not logically impossible; therefore it has a nonzero probability of happening. The task then is simply to figure out what that probability is. No further justification is necessary.

By contrast, a stable universe with fixed dimensions of spacetime with fixed properties prevents just “anything” from happening, because it greatly constrains what possible things can become actual, because the possible can only become actual by reconfiguring what’s there, and that has a probability defined by the structure of the thing itself. By contrast, when there is no thing, when there is absolutely nothing, that probability is defined by the structure of nothing, which structure is defined by what’s logically impossible; hence the logically impossible limits what can and can’t happen and thus defines the probability of what does, there being nothing else.

In short, there can’t be any state of nothing that doesn’t immediately become something; for the same reason, and in the same way, that there can’t be a four-sided triangle or a dog that is also and only a cat or the total absence of a pattern or regularity and so on. It’s simply impossible. Full stop.

BTW, as I mentioned upthread, the only hidden premises are logically necessary truths, and this includes:

P3.1: If C1 and P3, then C2.

In other words, P3.1: If nothing existed to prevent anything from happening or to make any one thing happening more likely than any other thing and of all the logically possible things that can happen when nothing exists to prevent them from happening, continuing to be nothing is one thing, one universe popping into existence is another thing, two universes popping into existence is yet another thing, and so on all the way to infinitely many universes popping into existence, and likewise for every cardinality of infinity, and every configuration of universes, then continuing to be nothing was no more likely than one universe popping into existence, which was no more likely than two universes popping into existence, which was no more likely than infinitely many universes popping into existence, which was no more likely than any other particular number or cardinality of universes popping into existence.

P3.1 is a logically necessary truth as shown in the subsequent analysis of P3 in the main post. That is why C2 follows from C1 and P3. (Obviously, if no thing is more probable than any other thing, and these are all the things, then none of these things can be more probable than the other.) I mention this to ensure formal completion of the argument. It should also be noted that P3 (and C2) as stated includes each “configuration” of universes, so not just the quantities are being counted (but it wouldn’t matter either way, C2 still follows whether you do or you don’t).

This is a very interesting argument, and I think it’s generally very persuasive. I have one question. (I don’t know whether it’s an objection, but at least it’s a question. And I’m only familiar with the basics of set theory and transfinite set theory, so there may be a simple answer to my question.)

You write (quoting your book),

If the probability of having any finite number of universes is always [approximately] 0 percent, then the probability that there is an infinite multiverse is [approximately] 100 percent.

Specifically, I see how the probability of any finite number of universes is always approximately 0 per cent, but I’m not yet sure about the inference to the proposition that the probability of there being an infinite multiverse is approximately 100 per cent.

I guess what I’m curious about is why we’re not treating any particular transfinite number as also just one potential value in infinity. I take it that the infinity in the denominator has to be the highest cardinality infinity, since we’re trying to ensure that that denominator is equal to all the possible values, where the values are the potential numbers of universes there are. For example, if we made the denominator simply aleph-null, that neglects the possibility that there are aleph-one universes, and so on. Thus I take it we’re using “INFINITY” to refer to the highest-cardinality infinity.

(I don’t think there is a highest-cardinality infinity, of course, which presents a related problem: that your denominator would actually be undefined. But we can set this aside for now.)

So now we can ask: What is the probability that there would be aleph-null universes? That alone would only be one in “INFINITY,” right? Now, what is the probability that there would be aleph-null or fewer universes? Isn’t that still just approximately zero, since INFINITY is infinitely larger than aleph-null? What is the probability that there would be aleph-one or fewer universes? Again, approximately zero, right?

Therefore, I think my worry is that any particular number of universes, including any transfinite number, will still always have only an approximately zero chance of occurring. It would follow (right?) that the probability of there being one universe (for example) is equal to the probability that there would be n universes, where n is any transfinite number.

Tom: Yes, the reason the term was stated (in the book) as a bold word (“INFINITY”) is that no specific infinity is meant. Pick any cardinality (as you note, there are infinitely many of them), and the conclusion still follows. In fact, there is no cardinality of infinity you can select, for which the conclusion does not follow. That is why the conclusion follows. (The reason is that there is no highest infinity. Thus an infinite proportion of the probability space is always apportioned to infinities, and not to finites.)

Thanks for your reply. I’m glad to see we’re on the same page about the INFINITY in the denominator.

There are still a few things I’m not sure about, however.

Suppose that a ‘multiverse’ refers to all of existence: all universes. ‘Finite multiverses’ comprise finitely many universes; ‘infinite multiverses’ comprise infinitely many universes.

Suppose that a multiverse cardinality (‘MC’) is a number that reports how many universes a certain multiverse comprises. You’re arguing that the MC that has obtained is almost certainly transfinite.

I take it that your argument depends on saying that there are infinitely many possible MCs, and so any particular finite MC has an approximately zero chance of being the correct one. (Right?)

I still don’t see how this argument doesn’t also apply to transfinite MCs: any particular transfinite MC also has a probability of approximately zero of occurring.

This may be crucial: Doesn’t it seem as if the number of possible MCs is equal to aleph-null? That is, couldn’t we assign each possible MC (including the transfinite ones) to a natural number? Assign 0 to 0, 1 to aleph-null, 2 to 1, 3 to aleph-one, 4 to 2, 5 to aleph-two, etc. If so, then even the disjunction of the transfinite MCs is no more likely than the disjunction of the finite MCs, right? It would follow that a finite number of universes is no less likely than an infinite number of universes.

Tom:Suppose that a ‘multiverse’ refers to all of existence: all universes. ‘Finite multiverses’ comprise finitely many universes; ‘infinite multiverses’ comprise infinitely many universes. Suppose that a multiverse cardinality (‘MC’) is a number that reports how many universes a certain multiverse comprises. You’re arguing that the MC that has obtained is almost certainly transfinite. I take it that your argument depends on saying that there are infinitely many possible MCs, and so any particular finite MC has an approximately zero chance of being the correct one. (Right?) I still don’t see how this argument doesn’t also apply to transfinite MCs: any particular transfinite MC also has a probability of approximately zero of occurring.

Yes, but that isn’t the relevant probability. The relevant probability is the number that will appear or less. For example, if there were only a hundred possible universes, and the number chosen was random (and we ignore configurations; counting those gets us to the same point, but not counting them makes the math easier), the probability that there will be 10 universes or less is 10%, whereas the probability of there being exactly 10 (i.e. no more, no less) is 1%. I am saying that 1/n is the probability of there being n or less (otherwise, we would be looking for 1/t, where t is the total number of all possibilities, not n). It is that which is infinitesimal for any finite number; which entails the remaining probability space (of there being more than n) equals 1 – {infinitesimal}, which is approximately 100%. By analogy, if the probability of 10 or less is 10% in the 100 universes example, then the probability of there being more than 10 in that same case is 90%; ergo if the probability of there being “any finite number or less” is infinitesimal, then the probability of there being some infinite number is 1 – {infinitesimal}, or approximately 100%.

There has been an argument called the “zero fit problem” which one can spin to the effect that because any infinitesimal probability is practically zero, all possible histories have a zero probability, and therefore our existence is impossible (because our particular world-history has a probability of effectively zero). This confuses not knowing its probability with its having none, and of course confuses infinitesimals with zero. But more importantly, it ignores the law of total probability (which is axiomatic but also follows necessarily from P2). The probability that some world-history will result is the sum of probabilities of all possible histories, which is 1, i.e. 100%. Therefore it doesn’t matter if the probability of “any specific outcome” is infinitely close to zero, because the probability that there will be one such outcome is 100%. That’s why the relevant probability is that of n or less, and not that of n.

[If you are interested in the debate about the zero-fit problem and why infinitesimal mathematics actually does solve it, see Adam Elga, “Infinitesimal Chances and the Laws of Nature,” Australasian Journal of Philosophy 82.1 (2004): 67–76, and the able refutation by Frederik Herzberg, “Internal Laws of Probability, Generalized Likelihoods and Lewis’ Infinitesimal Chances–-A Response to Adam Elga,” British Journal for the Philosophy of Science 58.1 (2007): 25–43. Herzberg uses nonstandard analysis, but I don’t believe that is necessary–it’s just one way to demonstrate the same point.]

Doesn’t it seem as if the number of possible MCs is equal to aleph-null? That is, couldn’t we assign each possible MC (including the transfinite ones) to a natural number?

It was that same fallacious reasoning that prevented people from realizing that there were greater quantities than aleph-null. For example, take Cantor’s Diagonal Proof: we can assign one MC outcome to every element on the bootom line of the diagram, yet there are morer elements in that line than in the infinite number of lines above it. There are therefore infinitely many more quantities than the natural numbers can count. So, no. You can’t assign one MC to every natural number and exhaust all possible MC’s. Cantor proved that impossible quite some time ago.

Thanks for all your replies. I think I have a much clearer idea of the argument.

I hope you have time to answer one more question for now.

Suppose N is the set of all possible MCs. (Recall that an MC for some multiverse reports the number of universes that the multiverse comprises.)

I’m still worried that set N will only have a cardinality of aleph-null. We know it can’t be less than aleph-null, since it includes all the natural number MCs. But why is it more?

I suggested a 1-to-1 correspondence between natural numbers and MCs, as follows:
0 – 0 universes
1 – aleph-0 universes
2 – 1 universe
3 – aleph-1 universes
4 – 2 universes
5 – aleph-2 universes,
and so on, generating an infinitely long list at which every natural number appears on the left hand side, and (I claim) every natural number and every transfinite number appears on the right side.

Now, to make a diagonalization-style argument against this correspondence, wouldn’t you have to show that there is a number that cannot appear on he right-hand-side here? How exactly would you do that? (If you could show there are aleph numbers between any two aleph numbers, that wouldn’t even be enough, since (e.g.) you can’t use a diagonalization proof to prove there are more rational numbers than natural numbers.)

You suggest assigning one MC to each element on the bottom line of the original diagonalization proof. I originally thought of trying to do that, but I decided that I couldn’t see how it would work.

If we’re imagining an infinitely long decimal expansion in base INFINITY, we could imagine a different MC at each digit. But that would be a set of MCs assigned to a natural number, not a single MC. I’m suggesting assigning a single MC to each natural number. A set of MCs wouldn’t itself be an MC, and I’m trying to count possible MCs, not possible sets of MCs.

Tom:Now, to make a diagonalization-style argument against this correspondence, wouldn’t you have to show that there is a number that cannot appear on he right-hand-side here? How exactly would you do that?

Cantor already did it. So I’m not sure what you don’t understand. Transfinites are numbers. They are in fact numbers that do not exist in the set of natural numbers.

If we’re imagining an infinitely long decimal expansion in base INFINITY, we could imagine a different MC at each digit. But that would be a set of MCs assigned to a natural number, not a single MC.

What you are trying to imagine doesn’t make any sense. Ignore “numbers” as digits (that is an artificial human language). Instead, think of elements and sets. There is a set of all natural numbers, and there are sets that can be placed in one-to-one correspondence with that set. Those sets have a quantity aleph-0. But there are also sets that can’t be placed in one-to-one correspondence with that set, sets that have more elements in them than all the natural numbers (yes, more than infinitely many numbers, even though there is no such thing as a highest number, yet there is still a greater quantity of elements than that; yes, this is weird; yet it is formally proven to be true). Aleph-1, for example, has at least one more element in it than the set of all natural numbers. Aleph-2 has at least one more element in it than Aleph-1. And so on.

If a set can have one more element in it, and a universe can be an element (and it can), then there are sets of universes to which no natural number can be assigned, i.e. the number of universes in that set is greater than any natural number. Again, even though there is not “supposed” to be a number higher than the highest number, because there is no highest number, yet Cantor’s proof proves that in fact there is. This is hard for human meat brains to wrap their heads around, but there it is. It’s nevertheless true.

We then call those numbers (those “extra” numbers) the transfinites or the hyperreals, to distinguish them from the naturals or the reals. Just as there are “imaginary numbers” (and there are; they really exist, geometrically, see Nahin’s An Imaginary Tale), so there are also yet more numbers not among the natural or real numbers. Another way to think of it is that there are numbers that can’t be placed on any number line, no matter how infinitely long it is. The square root of negative one is one such number (as a rotation operator, it exists out of phase with any standard numberline, i.e. it exists just outside the numberline, which is geometrically where you would end up if you “jumped” from a real number to an imaginary one; such “jumping” physically occurs in electrical fields, hence the square root of negative one is not just a human invention but a “real” quantity in the metaphysical sense). The hyperreals are another such number: there is nowhere to put them on a numberline. They nevertheless really do exist (in the sense that, there can be hypperreal quantities).

I know about Cantor’s diagonalization argument and I understand that there are different cardinalities of infinity.

Can we return to the one-to-one correspondence I mentioned a moment ago? Let N be the set of natural numbers and U be the set of possible quantities of universes in the multiverse. (Every element of U will be a quantity, but it may be finite or infinite.) Let A be the union of set N and the set of aleph numbers. (It seems to me that the cardinality of A will be aleph-0, but if it’s not, that would be important.)

Our question: What is the cardinality of U? In other words, how many different populations of universe can the multiverse have? It will be infinite, but what size of infinity? I’m suggesting that U = A, which would apparently make the cardinality of U aleph-0 as well.

So we list every element of N on the left, and make each correspond to a possible quantity of universes in the multiverse. I suspect that we have listed every element of U on the right side:

Now clearly, Cantor did not show that there was a quantity of universes that would not appear on the right hand side. And the standard Cantorian argument wouldn’t work, because there cannot be irrational quantities of universes. (π universes couldn’t possibly exist.)

It seems to me, then, that in order to argue that there are more than aleph-0 possible quantities of universes in the multiverse, I guess you’d have to say that there is some number Q (some quantity of universes) that is an element of U but not an element of A. And note that Q cannot be a fraction, nor an irrational number, nor a negative number, nor an unreal number, for obvious reasons. But if it’s a natural number or an aleph number, it’ll be in A.

Tom:I’m suggesting that U = A, which would apparently make the cardinality of U aleph-0 as well.

Why?

You have presented no proof of this. And your appeal to irrational numbers is wholly irrelevant. I told you to stop focusing on human languages and focus only on elements and sets. Cantor’s proof follows for any discrete elements whatever. Let’s make them apples of different shapes. Pretend digital numbers don’t exist. Pretend all human languages don’t exist. How many possible apples are there? Is it limited to A? Why?

First we start by counting up every string of possible applies in Cantor’s diagonal proof. Then we get to the bottom and see there are even more applies we can keep adding. Therefore there are more possible applies than A. As for applies, so for universes.

Again, ignore digits. Reproduce Cantor’s proof with elements (traditionally, set theory works with empty sets as the basic elements, i.e. {}, and nothing else, e.g. no “irrational numbers,” no numbers at all in fact). Then see what follows.

so the probability that there are is exactly what that probability would be if the number of universes that exist were selected at random. Of all the possible conditions that could obtain (no universe; just one universe; two universes; three; four; etc., all the way to infinitely many universes), that there would be only one universe is only one out of infinitely many alternatives. This entails it is effectively 100 percent certain an infinite multiverse exists because the probability of there being only one universe is then 1/INFINITY,

This particular ‘at random’ assumes equal probability across all numbers of universes; to be random doesn’t necessarily imply all outcomes are equally probable. Indeed there’s no distribution can do so – you can’t assign probabilities to the integers in such a way as to make them equally likely. It’s not coherent except as a limiting process. You effectively build into such a scenario the bias toward more universes than any finite number by the way you’ve defined ‘at random’ there. It also breaks some axioms of probability, so you’ll have to build new ones.

Efrique: Regarding the argument you linked us you (thanks for that!), you can assign probabilities to the integers in such a way as to make them equally likely, when you use infinitesimals of a corresponding cardinality. This is actually a geometric problem, not a problem in number theory. The question is: can you divide an area into infinitely many areas of equal size. The answer is yes, and remains yes for any cardinality of infinity.

For example, you can divide a space into an aleph-0 number of equally sized sections if each section has a proportional area equal to the aleph-0 infinitesimal. Likewise an aleph-aleph number of sections, if each section is an aleph-aleph infinitesimal. And so on for all cardinalities. Mathematically, {aleph-0} x {aleph-0-corresponding infinitesimal} = 1 (just as any {n/m} x {m/n} = 1). And yet every single slice is exactly the same size (the same exact infinitesimal), therefore exactly the same probability (which is produced by the ratio of that section’s area to the area of the whole space).

I think you are also confusing two different things: the actual determining of the probability, and there being one. We might not have the mathematical means to determine what the probability is of any particular number being selected. We can see it would be an infinity of infinities close to zero, and as there is no highest infinity, the actual probability cannot be defined. But that does not mean it does not exist (its existence, after all, can be logically proven, using the proofs of infinitesimal cardinality in the sources I referenced above). So there is a difference between knowing it exists, and knowing what it is.

I’m not sure what you mean. But if my guess at what you mean is right, then yes. Every spontaneous possibility exists, none more likely than the next, so one must then just divide the probability space among them, to ascertain what will actually exist.

Jean:There is something I don’t get about P2: while there is nothing to prevent anything from happening, there is also nothing to cause anything to happen. So why would anything happen?

Your invalid assumption here is that it is logically necessary for everything to have a cause. That is untrue. Causation is not logically necessary (or at least, to my knowledge, no one has ever proved it is). Therefore “nothing” does not have to “cause” anything, in order to produce everything. It just happens, uncaused. Precisely because no law of causality exists, when nothing exists.

I think that where your argument goes wrong is in treating nothing as something that needs to be limited by something else. Nothing is not some pulsating something of potential that is being held back somehow, but rather it is nothing. Only something can have possibility associated with it, and that possibility can be actualized or inhibited by something else. Utilizing these categories with regards to nothing just seems to misunderstand what absolute nothing is supposed to be, or not be.

dguller:I think that where your argument goes wrong is in treating nothing as something that needs to be limited by something else. Nothing is not some pulsating something of potential that is being held back somehow, but rather it is nothing. Only something can have possibility associated with it, and that possibility can be actualized or inhibited by something else. Utilizing these categories with regards to nothing just seems to misunderstand what absolute nothing is supposed to be, or not be.

As noted upthread, your definition of nothing is logically impossible. Therefore no such kind of nothing can exist. It is therefore not relevant. Either P1 is false, or P2 is true. There’s no getting around it. You have to pick one or the other.

As noted upthread, your definition of nothing is logically impossible. Therefore no such kind of nothing can exist. It is therefore not relevant. Either P1 is false, or P2 is true. There’s no getting around it. You have to pick one or the other.

Or maybe both are false?

I agree that P1 is false, because the fact that there is something means that there cannot ever have been nothing, because from nothing, nothing comes.

P2 says: “If there was absolutely nothing, then (apart from logical necessity) nothing existed to prevent anything from happening or to make any one thing happening more likely than any other thing.” I disagree with P2, because I do not think logical categories apply to absolute nothing, which is supposed to be bereft of any properties whatsoever, including logical ones. After all, logic depends upon determining the relationships between propositions, and if there was absolutely nothing, then there would be no propositions all, and without propositions, there is no logic.

Furthermore, when you say that “nothing existed to prevent anything from happening”, that does not seem to include the fact that if there is nothing, then nothing will happen, and thus the fact that there is nothing is preventing anything from happening, depending upon how you want to parse “prevent”. So, it might be the case that P2 is equally false, as construed.

I think that your conclusion depends upon your idea that absolute nothing contains the potential for anything and everything not logically contradictory. However, absolute nothing has no potential, because potential depends upon actuality. Potential has to do with something’s nature, and nothing has no nature, because absolute nothing has no properties that could define its nature.

dguller:[Re “Either P1 is false, or P2 is true. There’s no getting around it. You have to pick one or the other.”] Or maybe both are false?

If P1 is false, then the last paragraph of my post applies. The rest is only what must be the case if P1 is true.

I agree that P1 is false, because the fact that there is something means that there cannot ever have been nothing, because from nothing, nothing comes.

Unless you can prove that it is logically necessary that nothing comes from nothing, your latter assertion is false. That’s exactly the point of my entire post. Your argument is unsound, because your premise is not established to be true.

P2 says: “If there was absolutely nothing, then (apart from logical necessity) nothing existed to prevent anything from happening or to make any one thing happening more likely than any other thing.” I disagree with P2, because I do not think logical categories apply to absolute nothing, which is supposed to be bereft of any properties whatsoever, including logical ones.

Then you are saying that it is possible for logically necessary things to not exist, which contradicts logic (because if they could not exist, then they would not be logically necessary).

I already address that lunacy in the post. All sane people recognize that logically impossible things cannot exist; and a state in which logically necessary truths were false would be logically impossible. If “nothing” is a state in which logically necessary truths were false, then “nothing” would be logically impossible. And in that event, P1 is false. But it is only false for a definition of “nothing” in which not even logically necessary things exist, and that is not the definition I employ in P1. Therefore, P1 is logically possible (because it does not exclude the existence of logically necessary things). And P1 in that case entails P2. Therefore, you cannot object to P2 on the grounds that “nothing” lacks logically necessary things (“properties” as you call them). It must necessary have those properties, because it is logically impossible that they would not exist.

After all, logic depends upon determining the relationships between propositions, and if there was absolutely nothing, then there would be no propositions all, and without propositions, there is no logic.

You are confusing propositions, which are about things, with the actual things they are about. A logically impossible proposition describes a logically impossible state of being. A state of being in which logically necessary things don’t exist is itself impossible. Propositions don’t have to exist for that to be the case, any more than words must exist for the things they describe to exist.

(In fact, in proper terminology, “proposition” refers in the abstract to the arrangement of ideas contained in all possible “statements” that have the same meaning; as such, propositions don’t really exist at all, except in their instantiations as statements–otherwise they are a hypothetical construct we invented; only that which propositions refer to exists, i.e. only that which all “hypothetically possible statements that have the same meaning” refer to exists in actuality. Propositions can exist potentially, but then we’re no longer talking about what actually exists. And we can conflate propositions with what they are about, but if we do that, all propositions exist when the things they are about exist. Therefore, in that connotation, all propositions about “nothing” exist when “nothing” exists. That is, it is logically impossible to separate “nothing” from all true propositions about “nothing.” My argument thus proceeds.)

Furthermore, when you say that “nothing existed to prevent anything from happening”, that does not seem to include the fact that if there is nothing, then nothing will happen, and thus the fact that there is nothing is preventing anything from happening, depending upon how you want to parse “prevent”. So, it might be the case that P2 is equally false, as construed.

You are no longer making logical arguments at this point. It is not a “fact” that “if there is nothing, then nothing will happen.” Unless you can prove that to be logically necessary, which you haven’t done. Instead, “if there is nothing, then nothing will happen,” is only one possible thing that can happen. And it is no more likely than any other possible thing. That’s my point.

I think that your conclusion depends upon your idea that absolute nothing contains the potential for anything and everything not logically contradictory.

Yes. Because (as I explain in the post) any other “nothing” is logically impossible and therefore can’t ever have been. Which means the only kind of “nothing” that can ever have been is one that “contains the potential for anything and everything not logically contradictory.” That is the only kind of nothing that is logically possible, therefore it is the only kind of nothing on which P1 can ever have been true (well, except for “nothings” that contain even more than that, hence my point about Krauss et al., which I define as not nothing; so you can say that P1 refers to the most “nothing” nothing that can possibly exist; all other nothings being either more something, or impossible).

However, absolute nothing has no potential, because potential depends upon actuality. Potential has to do with something’s nature, and nothing has no nature, because absolute nothing has no properties that could define its nature. Any thoughts?

I’ve already answered this claim in the main post and in the comments above. So you are just talking in a circle at this point. You have not proved that “potential depends upon actuality” (other than the actuality of what is logically necessary) or that “nothing has no nature” (by definition it must have a nature: that which makes it nothing rather than something, which nature I describe in detail) or that “absolute nothing has no properties” (it must have all logically necessary properties–unless, again, you care to insist that logically impossible things can exist). So you need to take seriously what I have already said, before continuing to issue unproven statements as some sort of fallacious Argument by Gainsaying.

I already address that lunacy in the post. All sane people recognize that logically impossible things cannot exist; and a state in which logically necessary truths were false would be logically impossible. If “nothing” is a state in which logically necessary truths were false, then “nothing” would be logically impossible.

Nothing is a “state” in which logic is not supposed to apply at all, because not even logic exists in absolute nothing. If logic existed, then it would not be absolute nothing, because something (i.e. logic) exists, which you agree with. So, its not that in absolute nothing logical impossibility occurs, neither logical necessity nor impossibility occurs, because logic does not apply to absolute nothing, because logic does not exist in absolute nothing, because nothing at all exists in absolute nothing. At least, that’s my understanding of the traditional nothing of ex nihilo.

dguller:Nothing is a “state” in which logic is not supposed to apply at all

I’m calling a stop to this. You keep arguing by assertion. That’s simply illogical. Until you prove that nothing is not governed by logic, you have presented no reason to believe it. Just asserting it over and over again is not a proof.

I already showed upthread that you are here confusing logic as the human language with the facts logic describes. Those are not the same thing. By definition the facts logic describes cannot ever “not apply” unless logically impossible things can exist. In other words, to say “logically impossible things cannot exist” is to say that logic is always true (because it always describes what does or doesn’t exist).

Thus logic will only not apply to nothing if logically impossible things can exist. So are you asserting that logically impossible things can exist?

Also, just so you know, there is a discussion of your ideas at…

Note to everyone: I do not have time to wade through other threads. If you have valid criticisms or questions, post them here. Otherwise, I have neither time nor interest. Sorry.

I’m calling a stop to this. You keep arguing by assertion. That’s simply illogical. Until you prove that nothing is not governed by logic, you have presented no reason to believe it. Just asserting it over and over again is not a proof.

As I mentioned earlier, the laws of logic are abstracted from the regularities and patterns in reality. It is from reality that they get their grounding and justification, and when you take away reality, then they lose their grounding and justification, and do not apply anymore. They seem to always apply to all scenarios to us, because they apply to everything around us, but that’s the point. We are embedded within reality, and not absolute nothingness, and thus from our perspective the laws of logic are universal. However, they are universally applicable to reality, which does not mean that they are equally applicable to absolute nothingness, which is supposed to be the antithesis of reality.

You argued earlier that even absolute nothingness has underlying patterns and regularities, and thus must have a logic to it. But there are a few problems with this claim. First, the patterns and regularities of absolute nothingness are not necessarily the same as the patterns and regularities of reality, which is all we actually know about. Second, you can only have a regularity within space-time, because there is something that must persist from one place and moment to the next. But there is no space-time within absolute nothingness, because there is absolutely nothing there, and space-time is something. Third, if you want to say that there is a regularity within absolute nothingness, then the only regularity would be that from nothing, nothing comes, which is the ex nihilo principle itself. Thus, conceding regularity also concedes the validity of the ex nihilo principle.

I already showed upthread that you are here confusing logic as the human language with the facts logic describes. Those are not the same thing. By definition the facts logic describes cannot ever “not apply” unless logically impossible things can exist. In other words, to say “logically impossible things cannot exist” is to say that logic is always true (because it always describes what does or doesn’t exist).

By definition absolute nothing does not contain anything, including the laws of logic, which are something. Sure, the laws of logic demand that there must be something even in absolute nothing, but what do you expect? They get their traction from reality, and thus necessarily must endorse reality everywhere. It is like wearing dark glasses, and seeing dimness everywhere.

Thus logic will only not apply to nothing if logically impossible things can exist. So are you asserting that logically impossible things can exist?

Logically impossible things cannot exist in reality, which consists of things. Nothing has no things, including logically necessary, possible or impossible things. Again, logic applies to reality, i.e. the totality of things, but does not necessarily apply to the “state” of no things.

I do not have time to wade through other threads. If you have valid criticisms or questions, post them here. Otherwise, I have neither time nor interest. Sorry.

That’s fine. I only mentioned it, because on that thread was a mathematician who contests your use of mathematics in your argument. His argument was above my pay grade, but he seemed pretty sure that you had made some fundamental mistakes in your mathematical reasoning.

dguller:The laws of logic are abstracted from the regularities and patterns in reality.

To be more correct, the laws of logic describe one singular fact: that logically impossible things cannot exist. Translation: logically contradictory states cannot exist. If “nothing” ever exists then no property or outcome of that “nothing” can be logically contradictory. From that fact my argument follows.

However, they are universally applicable to reality, which does not mean that they are equally applicable to absolute nothingness, which is supposed to be the antithesis of reality.

“Supposed to be” is a phrase you keep using. You seem to think it means “is logically proven to be.” And thus you use it as an excuse to argue by assertion, without ever proving any of your assertions true.

I am getting tired of this. Make an actual valid argument, or give this up. Because you are wasting my time and everyone else’s time here.

Nothing is as much a state of reality as anything else. For example, “in reality there was once nothing” is not a logically contradictory statement; neither is “a state of nothing really existed” or “a state of nothing was once the reality” or “a state of nothing is real,” all as opposed to “fictional” or “false” or “non-existent.” If “a state of nothing did not exist” then nothing was not reality. But if a state of nothing did exist, then once upon a time nothing was reality.

If you can present a formal syllogistic proof otherwise, do so. If not, then stop asserting what you cannot prove.

First, the patterns and regularities of absolute nothingness are not necessarily the same as the patterns and regularities of reality, which is all we actually know about.

Since I don’t infer any properties of nothingness from “the patterns and regularities of the reality we actually know about,” this is a moot point. I infer all its properties from logical necessity, i.e. the only “patterns and regularities of absolute nothingness” I affirm are those that are logically necessary, not those that are empirically inferred from something else (that would describe Krauss’s “nothing,” not P1’s “nothing”).

Second, you can only have a regularity within space-time, because there is something that must persist from one place and moment to the next.

This statement shows you aren’t paying attention. Because it is exactly the same thing I said. Go back through our thread in comments above until you figure out how I affirmed exactly the same thing, and why it entails P2 when there is no persisting space-time.

But there is no space-time within absolute nothingness…

Unless the existence of space-time is logically necessary. See my discussion of this in the original post (which you should have read by now, so I wonder why I have to tell you this).

Third, if you want to say that there is a regularity within absolute nothingness, then the only regularity would be that from nothing, nothing comes, which is the ex nihilo principle itself.

Prove it.

I think I’ve asked you to do this three times now. Instead you just keep asserting it. Assertion is not an argument.

Present a formally valid syllogism demonstrating that the only logically possible thing nothing can do is nothing.

Until you can do that, you are not being logical.

By definition absolute nothing does not contain anything, including the laws of logic, which are something.

Holy Christ. Are you serious? I went over this, here and in the original blog. The only state of nothing that is logically possible is a state of nothing in which logically necessary truths still obtain. Therefore, your statement above is false. It is only true of a logically impossible state of nothing, which, by virtue of being logically impossible, can’t ever have existed (therefore P1 can never be true on your definition of nothing; and I am only interested in exploring logically possible hypotheses, which requires my definition of nothing in P1, not yours; my definition is logically possible, yours is not).

Logically impossible things cannot exist in reality, which consists of things. Nothing has no things, including logically necessary, possible or impossible things.

That is impossible. If something necessarily exists, there can’t ever have been a scenario in which it didn’t exist. Therefore, if nothing has no things not even logically necessary things, then we have a state of being in which things that cannot not exist, do not exist, which is logically impossible. Therefore, you do seem to be asserting that logically impossible things can exist. So, are you going to admit this? Or are to going to keep repeating yourself and avoiding the question?

Perhaps you are confusing logically necessary things that follow from existing things, with logically necessary things that follow from nothing. I do not assert that any of the former obtain on a state of nothing, only the latter. I am very specific about this in the original post.

His argument was above my pay grade, but he seemed pretty sure that you had made some fundamental mistakes in your mathematical reasoning.

Ask him to present it here, and ask him to avoid formal symbolism and just explain his point in plain terms so the maximum number of people can understand it.

Your argument is a rather more sophisicated version of the one I have been using. More crudely: The universe cannot come from “nothing” if the state of “nothing” includes a “god” who is “something”. It is more likely that the universe came from “nothing” that contained the simple brute potential for “something”. “Simple brute potential” is not something that theists would be happy to define as “god”.

Thomas Atwater:There’s a dead link in it though: At the very end of the 3rd paragraph (the paragraph which begins, “I am an empiricist . . . .”), in parentheses: “as I’ve explained before”. Perhaps this can be fixed.

Done. Thanks!

(Reload the page next time you view it and the corrected code will load.)

Hi Richard,
I have several questions that I hope you have the time and inclination to address. One has to do with this statement: “However, since it is logically impossible for logical truths not to exist, if logical truths must exist at some point in spacetime, then it would follow that spacetime is logically necessary and therefore there can be no “absolute nothing” that lacks at least a singular point of spacetime (which is of course practically nothing).” But that singular point of spacetime is nevertheless something, and you have just argued against the logical possibility of P1. Without P1, you’ve got nothing! (Pun intended.)

What do you mean by “a singular point of spacetime”? Space is a meaningless concept without objects in the space. Time is a meaningless concept without objects to persist in time. And as you say, once you have spacetime, you have limitations on what can exist. So which is it, we start with no spacetime or just an itty-bitty spacetime (whatever that means)? In my mind, it makes much more sense to say that if you start with nothing except for the laws of logic and probability (and they don’t “exist”, they are merely applicable), then nothing will exist because there is no spacetime for them to exist in. So if you start with nothing, it is logically impossible for anything to exist.

You seem to be blissfully unaware of how counterintuitive your argument above is. Here’s an example to make that more apparent: It is logically possible for a three-legged fire-breathing purple giraffe with green polka dots to exist. If we start from nothing, then there is nothing to prevent this giraffe from existing, therefore it is possible for it to exist. Indeed it is equally possible for 0,1,2,3..on into infinity of them to exist. According to the rules of probability then if we start with nothing, we must end up with an infinite number of three-legged fire-breathing purple giraffes. Do you realize how ridiculous that sounds? (A previous note suggested that you use this argument in a debate with a Christian, I would advise against it: It would be very easy to make it sound absurd.)

We don’t even have to talk about infinity. When you say that it is equally probable for 0 or 1 purple giraffe to exist, you lose me. It makes no sense to take about the probability of an event without any basis upon which to assign probability. If you don’t have spacetime, nothing can exist by definition. If you do have spacetime, you have restrictions on what is possible and the two different possibilities are not equally probable.

Also nothing exists (except for logic and probability which do not really “exist”, but are always applicable) outside of spacetime. Thus spacetime does not really “exist” in the same way either, unless there is a meta-spacetime for it to exist in. In the same way, a universe does not “exist” unless there is a meta-spacetime to exist in. We talk about our own universe being 14 billion years old, but what we mean is that there have been objects in the universe that long. I think it would add some clarity if you talked about what you meant by a universe “coming into existence”. Do you mean appearing suddenly in a meta-spacetime? Can there be meta-meta-meta spacetimes with infinitely many metas? Could there be something entirely different than spacetime that we are unaware of, that makes it possible for things to exist? But then we would be so far into speculation that our terms become vague to meaningless.

garyfletcher:But that singular point of spacetime is nevertheless something, and you have just argued against the logical possibility of P1. Without P1, you’ve got nothing! (Pun intended.)

No, the word “nothing” in P1 is defined in that post as being nothing but the existence of logically necessary things (because anything less than that is logically impossible, thus the only way P1 can ever be true is on the definition I end up with). That you are asking this question suggests you did not read the blog post. That’s a big no no. Go and read the thing first before asking questions.

What do you mean by “a singular point of spacetime”?

Nothing more than a place and time to be. In other words, insofar as logically necessary things exist, they must exist somewhere at some time, otherwise they exist never and nowhere, which is synonymous with not existing, which is logically impossible. Geometrically, a single point of spacetime is simply a single place of existence (it is the 0 point on an x-y axis where x is space and y is time). But as I note in the post, that is practically nothing. Hence I agree with the conclusion that, if in fact such a point’s existence is logically necessary, then indeed that is for all intents and purposes still almost nothing.

Space is a meaningless concept without objects in the space.

That’s not true. Empty space is logically possible.

Perhaps you are confusing the existence of space, with the existence of reference frames (e.g. velocity is meaningless without objects in space).

Time is a meaningless concept without objects to persist in time.

That’s also not true. Just as empty space is logically possible, so is the passage of time in that space. It is easy to model an empty four-dimensional volume of space-time (locations then exist relative to each other).

Perhaps, again, you are confusing the existence of time with the existence of reference frames.

So which is it, we start with no spacetime or just an itty-bitty spacetime (whatever that means)?

Whatever is logically necessary. Nothing more. Precisely as I argue (hence again, it does not look like you have read this blog).

So if you start with nothing, it is logically impossible for anything to exist.

Prove it. With a formal and valid syllogism. Until then, this is just argument by assertion, not logic.

You seem to be blissfully unaware of how counterintuitive your argument above is.

I am very aware of how counterintuitive it is. I just know (as you should too) that many counterintuitive things are nevertheless true. (See the discussion of infinite numbers in this comment thread for example.)

It is logically possible for a three-legged fire-breathing purple giraffe with green polka dots to exist. If we start from nothing, then there is nothing to prevent this giraffe from existing, therefore it is possible for it to exist.

To be more correct, a space containing (or giving rise to) material with the required properties that is organized into that giraffe is possible. That would indeed be one possible universe: a space in which such a giraffe exists and nothing else.

What then happens in or to that universe will depend on what other properties it randomly has, e.g. if the space is small and the giraffe has the same properties as our giraffes, which includes graviton production, then that universe will collapse gravitationally, crushing the giraffe into atomic goo, almost instantly. Under vastly accumulating pressure at sub-quantum scale, it will then likely explode into an expanding universe containing raw materials and no evidence of there having been a giraffe.

Can there be a stable giraffe-only universe? Possibly. You’d have to work out with a cosmologist all the properties that that universe will have to have, and they will probably be an amazingly vast and bizarre set of coincidences, making that universe one of the rarest of all possible. But if it’s possible, it’s possible. See my discussion of Boltzmann brains and gods in my follow-up post.

Indeed it is equally possible for 0,1,2,3..on into infinity of them to exist. According to the rules of probability then if we start with nothing, we must end up with an infinite number of three-legged fire-breathing purple giraffes.

That’s not necessarily true (the math is a bit more complicated; and by the argument given here, it is not the case that all possible universes will exist, but that an infinite number of them will exist, randomly selected from all possible). But yes, it might be true. Just as it is true that infinitely many Boltzmann gods will exist (in universes other than ours; see, again, my follow-up).
Do you realize how ridiculous that sounds?

It isn’t ridiculous. Ridiculous means worthy of ridicule. That which is logically necessary is not worthy of ridicule. You seem to be relying on a fallacious “that’s weird, therefore false” rule of inference here. Something being weird, even appallingly weird, does not make it false. It doesn’t even make it improbable.

Present an argument that it is improbable or false, then we’ll talk. Otherwise, you are just using a fallacy called “Reductio ad Ridiculum.” It’s a fallacious form of the otherwise-valid Reductio ad Absurdum, which only has validity when the conclusion is logically impossible. But here, even if you could show this giraffe universe to be logically impossible, all that would do is eliminate it from all possible universes (some cosmologists actually claim they can do this to all universes but ours, i.e. they claim that our universe and its physics is the only logically possible one; I have yet to see that, but all the power to them if they can). Otherwise, if it’s possible, it’s possible. You can’t really escape from that fact. The real question is, why do you want to?

Thank you very much for your reply, Dr. Carrier. I assure you that I have read the whole article, and this time I’m attempting to ask better questions. The first question is, why is it logically necessary to have spacetime in your definition of “nothing”? You seem to argue that the laws of logic must be true, and therefore they must exist, and if they are going to exist, there must be spacetime: “However, since it is logically impossible for logical truths not to exist, if logical truths must exist at some point in spacetime, then it would follow that spacetime is logically necessary and therefore there can be no “absolute nothing” that lacks at least a singular point of spacetime”. I agree that the laws of logic must be true, but I don’t see that it follows that they must “exist” in a spacetime. As you point out, they don’t exist in the same way as aluminum-titanium alloy, they only exist in the sense of being true. It is not necessary to appeal to anything existing to prove that the angles in a triangle in a flat plane add up to 180 degrees. It would seem that the laws of logic are true independently of any spacetime and would be true in the absence of spacetime. Therefore it is logically possible for logical truths to exist (that is, be true) without the existence of spacetime.

I’m a bit worried by the definition of a spacetime without objects, which is part of the “nothing” as defined in P1. On subject of space Wikipedia says that “disagreement continues between philosophersover whether it [space] is itself an entity, a relationship between entities, or part of a conceptual framework…the metaphysician Immanuel Kant said neither space nor time can be empirically perceived, they are elements of a systematic framework that humans use to structure all experiences.” On the subject of time it says, “…defining it [time] in a non-controversial manner applicable to all fields of study has consistently eluded the greatest scholars. A simple definition states that “time is what clocks measure””. If there is uncertainty in the definition of these terms, then it would seem that we could not use them in a logical proof, especially if the proof requires spacetime without objects, and it’s not clear that the terms “space” and “time” have meaning without objects.

A difficult logical step in the proof for me is P2. I can understand all events that are logically possible being possible, but not to move from there to any event being equally probable. Yes, there is nothing to stop any event from happening, but how does that determine the probability of any of them happening? No doubt my problem is that this is a highly unusual way of thinking. I am familiar with assigning the probability of an event based on observations and/or knowledge of physical forces involved or of hypothetical situations in which the probability is given. I’m not sure if it’s meaningful to assign probability based on possibility and there being nothing to prevent the possibility. But I understand that you have replied to this question before, and perhaps there’s nothing more for you to say…

There seems to be time involved when we go from “nothing” to the universes popping into existence. P1 says, “In the beginning”. Does that mean there is a point in time in which there was nothing, and then there are many possibilities that might “continue” from there? If there is a time in which there was nothing, doesn’t that mean there was more than “nothing”? Or is the time in which the singular point of spacetime exists and then all the universes pop into existence that singular point of spacetime? How much time between “nothing” and an infinite number of universes? Any arbitrary amount of time?
I look forward to your illuminating replies!

garyfletcher:I assure you that I have read the whole article, and this time I’m attempting to ask better questions. The first question is, why is it logically necessary to have spacetime in your definition of “nothing”?

But if you had read the whole article, you would already know my answer to this question. I will quote the article you claim to have read (your own quote even omitted the entire argument…so I have to ask, how did you manage to overlook the argument, in the very act of quoting its conclusion?):

I have argued that that which exists at no location [see link] or at no point in time, by definition exists never and nowhere, which is by definition not existing. So one might think that if nothing exists, no place or time exists, therefore logical truths cannot exist. However, since it is logically impossible for logical truths not to exist, if logical truths must exist at some point in spacetime, then it would follow that spacetime is logically necessary and therefore there can be no “absolute nothing” that lacks at least a singular point of spacetime (which is of course practically nothing).

Formally, if A, then B; if B, then C; A, therefore B; therefore C. If A: logical necessity exists, then B: it exists at some place and time (as otherwise it exists never and nowhere, which is not existing); if B: there is some place and time, then C: there is spacetime; A: logical necessity exists (because it is logically impossible for logically impossible things to exist or happen, and logical necessity is simply the fact of logically impossible things not existing or happening, therefore if logically impossible things cannot exist or happen, then by definition logical necessity exists), therefore B: there is some place and time; therefore C: there is spacetime.

If, of course, you can show that something can exist that nowhere exists and never exists (despite that being a self-evident contradiction), then you will have proved that logical necessity does not have to exist somewhere or at any time, in order to exist. Which would be in agreement with the rest of my argument. I only used this as an example of how logical necessity can entail unexpected conclusions about how much “nothing” can actually logically exist. But even taking that away would not change any of the rest of my argument. I would in fact be delighted if you could formally, syllogistically prove that something can exist that nowhere exists and never exists. That would be a profound discovery in basic ontology.

As you point out, they don’t exist in the same way as aluminum-titanium alloy, they only exist in the sense of being true.

They only exist in one single sense at all: in the fact that logically impossible things cannot exist or happen. Wherever and whenever it is true that A (logically impossible things cannot exist or happen), it is by definition true that B (logic governs what exists or happens). That’s it. There is no weird Platonic “logic fluid” we have to add to anything. It’s simply a fact of all existence and all possibility whatever.

I’m a bit worried by the definition of a spacetime without objects, which is part of the “nothing” as defined in P1.

This is an expression of incredulity, not logic. You are falling victim to the fallacy of replacing “logically true conclusions” with “what my intuition feels comfortable with,” which is wholly invalid reasoning. Indeed, I very specifically called that fallacy out in the original post, more evidence that you aren’t bothering to read my post at all carefully.

If there is uncertainty in the definition of these terms, then it would seem that we could not use them in a logical proof, especially if the proof requires spacetime without objects, and it’s not clear that the terms “space” and “time” have meaning without objects.

That’s a fallacious conclusion. If it were sound, then no logical argument of any kind whatever is valid (outside of hard math). Because there is uncertainty in the definition of any term (outside of mathematics).

Logic proceeds by defining terms, and then deducing what follows. Disputes over the definition are therefore irrelevant, except insofar as the dispute is over which definition of the term describes what actually exists, but that is a dispute not relevant here, where we are operating on hypothetical necessity, i.e. I am deducing what would be true if P1 is true, I am not asserting that P1 is true, so disputes over the definition of nothing are irrelevant to my P1 argument, as they can only concern whether P1 is true, not what follows if P1 is true.

Likewise here: it doesn’t matter that there are many definitions of space and time. All that matters is that on one of those definitions, spacetime necessarily exists. And that definition is as I stated upthread: nothing more than a place to be.

Insofar as someone might talk about spacetime in a different sense, they are simply not talking about what I was talking about, and therefore what they are saying is irrelevant to what I said.

I can understand all events that are logically possible being possible, but not to move from there to any event being equally probable. Yes, there is nothing to stop any event from happening, but how does that determine the probability of any of them happening?

I don’t understand this question. Perhaps you are asking about the Principle of Indifference. Epistemically, “when there is no knowledge indicating unequal probabilities,” then all probabilities are epistemically equal. This correlates to: metaphysically, “when there is no thing causing unequal probabilities,” then all probabilities are actually equal.

There seems to be time involved when we go from “nothing” to the universes popping into existence.

Not exactly. What happens will be decided instantaneously. In zero time. The appearance of nonzero time is then one of the things that happens. Thus, if we could trace the timeline back we would end up at a point with nothing in it, and from there we could trace the spontaneous appearance of nonzero timelines which extend from that zero point. The appearance of a universe at t = 1 is then simply the kind of thing that can inevitably happen the instant there is a t = 0. It would be like trying to type “T” and every single time it instantaneously comes out “T1″ on the screen, or T and some random number; you can’t ever type T and not instantly get the number beside it; yet the number is not occupying the same place as T. T occupies position 0. The number occupies a nonzero position. But since they are always inevitably bound, such that every time you have a T, you get a random number beside it, you can never just have T (thus you can never just have 0 time, according to my P1 argument). You don’t even have to think of it sequentially, but existentially (like WL Craig’s ontological causation vs. temporal causation: see my response to this same question upthread).

Carrier: But if you had read the whole article, you would already know my answer to this question. I will quote the article you claim to have read (your own quote even omitted the entire argument…so I have to ask, how did you manage to overlook the argument, in the very act of quoting its conclusion?):

Actually, I have read the whole article, and I do know what you wrote as an answer. Far from overlooking your argument, I quoted it because I wanted to concentrate on it. You seem to suffer from the misconception that if I ask a question about some part of your argument that I have not read it thoroughly. You need to entertain the possibility that I don’t understand it or don’t agree with it!

I agree completely with you that when we talk about the laws of logic existing, we mean something different than objects which exist in space and time such as aluminum alloy. I agree with your definition of what we mean by the laws of logic existing: “And here ‘exist’ means only in the sense of being true”. Thus when we use the word exist with regard to the laws of logic, considerations of space and time are irrelevant. That’s why I concentrated on the sentence, “if logical truths must exist at some point in spacetime”, because that’s the point at which it seems that you are disagreeing with your own definition of “existing” with regard to the laws of logic.

This same apparent contradiction appears in your answer to me: “ If A: logical necessity exists, then B: it exists at some place and time (as otherwise it exists never and nowhere, which is not existing)”, now you’ve switched to the usual definition of what it means for objects to exist in spacetime, contradicting the definition above. Further down you make a new definition, also independent of considerations of space and time: “They [the laws of logic] only exist in one single sense at all: in the fact that logically impossible things cannot exist or happen.”

So if I take either one of your definitions that do not take into consideration spacetime, and define nothing as a state of no spacetime, no objects, the laws of logic may still exist: By your first definition above, the laws of logic are still true, there’s just no objects around that must follow them. By your second non-spacetime definition, the laws of logic exist if logically impossible things cannot exist or happen. Well, that’s certainly true if nothing, including spacetime, exists!

I could go on to the other points, but since we’ve made so little progress, perhaps it’s best to just concentrate on one. I must say that usually you seem very logical to me, for example I enjoyed your book A Defense of Metaphysical Naturalism: Sense and Goodness Without God. And I enjoyed and followed the logic of your post criticizing Bart Ehrman’s post. It appears that he is attempting to marginalize you and other mythicists, but I thought you aptly criticized his reasoning in your post, and look forward to your review of his book. (Indeed, I studied an Ehrman textbook in a class and it appears that the mythicist-bashing Ehrman contradicts the old Ehrman!)

garyfletcher:Far from overlooking your argument, I quoted it because I wanted to concentrate on it.

But you didn’t quote it. That was my point. You quoted the conclusion, not the argument. Then you asked what my argument was!

You seem to suffer from the misconception that if I ask a question about some part of your argument that I have not read it thoroughly.

Only when you do what you did: quote a conclusion, and ask what the argument is, when the argument is exactly one line previous to what you quoted. How could you not have known what the argument was, thus necessitating asking me what it was? Evidently, by not reading the article carefully.

As to why spacetime must necessarily exist, I have answered that a dozen times already: because there can never be a state of nothing that is not governed by logic; logic cannot exist but for somewhere to exist; therefore there is always a minimal somewhere to exist (a zero point of space-time). You agree with the second premise. You seem not able to understand the first. That’s where you need to work on comprehending the point.

Well, we can agree on one thing! You have given the same answer over and over! The only trouble is you have never addressed my question. I realize you’re a busy man and don’t have the time to read all these questions carefully. Clearly you need some help (including some work on being patient and cordial), so I will put in most of an apt response, leaving only a small part for you to fill in.

Dear Gary: Although I defined logic existing thusly: “And here “exist” means only in the sense of being true”, I didn’t really mean to exclude the necessary stipulation that for logic to exist that there must be a space and time for it to exist in. I know that you have argued that logic is true even without space and time because it’s truth is not dependent on spacetime objects, but I don’t agree that that alone means that logic would exist because [and here you actually address my question, possibly explaining how you think the truth of logic is dependent on spacetime!].

At any rate, thank you for the close reading of my argument. In the future, to be clear, I will revise the above statement to read: “And here “exist” means in the sense of being true, as well as being somewhere in some place”.

Wrong again, Dr. Carrier! I haven’t ignored anything you wrote. I’ve read and carefully considered everything you’ve written. The places that refer to my question are in the original post in the paragraph that begins: “For instance, I have argued…”. Also there’s the paragraph in a note to me that begins, “Formally, if A, then B…” and the following paragraph. These arguments are very clear and do not need to be repeated. However, they all assume that the word “exist” when referring to logic means the same as the word means for an object. That is, for an object to exist, it must be somewhere in some time, it “exists” by being in spacetime.

But my question begins with your other definition of “exist” when referring to logic: “And here [referring to logic] “exist” means only in the sense of being true.” Thus I’m proposing that logic doesn’t have to exist in spacetime in order to exist, that is, in order to be true. We seldom speak of logic being in a certain place or existing in a certain time, logic is true independently of spacetime. This possibility you have never addressed—you just repeat your argument that logic must exist in spacetime, because the very definition of existence requires it. This obviously does not address my question, which assumes a different definition for “exist” when referring to logic.

I should add that to criticize me for not reading or ignoring what you’ve written is an assertion that you cannot prove unless you are able to read minds at a great distance. I assume you don’t claim that!

Here’s one way the argument could go: For logic to exist, all that it necessary is that it be true. We cannot imagine or even think logic is false, therefore there is no circumstance in which logic does not exist. However, we can easily imagine the circumstance of no space and time. Any circumstance we can imagine is possible if it has no illogical characteristics, no characteristics that logically contradict each other. The circumstance of no space and time has no characteristics to be logical or contradictory, except for the mandatory characteristic of logic existing (being true). Therefore the circumstance of no space and time is possible. Thus the circumstance of logic existing (being true) although there is no space and time is possible.

Now I suggest that you attempt to humble yourself a bit, give up the obviously false criticism that I have ignored what you’ve written, and get on with explaining why logic needs spacetime to be true (if you can).
Regards,
Gary

You have completely lost track of the original argument at this point. The comparison I made was between physical structure (atoms exist) and truth (such as that a region of spacetime potentially can have any shape–it does not have to have that shape for that potential to exist), and between logically true propositions being true (“cats exist”) and logically necessary propositions being true (“it is possible for cats to exist”). You are completely ignoring these distinctions, which are the ones I actually made. And in the process, you end up making points that have no relevance at all to whether my actual argument is valid or sound.

the adage ex nihilo nihil fit is just a formulation of the principle of sufficient reason. In particular this formulation limits itself to saying that certain kinds of things (eg, those that come into being / are made) have explanations or at least can’t come from nowhere.

You seem to have developed an argument that denies the principle of sufficient reason while relying on it. After all you seem to expect a reason to reject your denial of it; but this implicitly affirms the PSR. Odder still, you explicitly affirm ”that all the fundamental propositions of logic and mathematics are necessarily true (for example, all valid and sound theorems and syllogisms are necessarily true, in the sense that, when given their premises, their conclusions cannot be false”

Even if you want to deny the PSR as a fundamental proposition of logic, the metaphysical-cannot in your assertion ”when given their premises, their conclusions cannot be false” has no force absent it.

Again: ex nihilo nihil fit is just a formulation of the principle of sufficient reason – to deny it one must either implicitly affirm it, or deny the principle of contradiction and there is no more fundamental principle of logic than that.

vaughnbodie:The adage ex nihilo nihil fit is just a formulation of the principle of sufficient reason.

That’s not true. The ex nihilo argument predates Christianity (it was developed by the Presocratics and taken up by later pagan philosophers). The principle of sufficient reason was independently developed by the presocratics. They were not connected then, and I am not aware of when they ever were. The principle of sufficient reason only says that something must have a reason to exist. If nothing necessarily becomes something, then that satisfies the principle of sufficient reason. Therefore the principle of sufficient reason can be true when ex nihilo nihil fit is false. They therefore cannot be the same thing. And historically they never have been.

You are badly confused about what the principle of sufficient reason is. I suggest you read up on it.

In any case which theists deny that absolute nothing is logical impossibility?

Saying that out of nothing nothing is made does not affirm the actual existence of nothing. But you use this as spurious motivation to immediately redefine nothing to a “nothing” including only some logically necessary things.

”So if that’s what theists mean by “if there was no God, then there was once absolutely nothing,” that not even logically necessary things existed, then their claim is self-refuting. We can then dismiss it out of hand.”

Well not so fast. Theists (at least Thomists) insist that God is logically necessary. Whatever you think of the quinquae viae not one of them claims God is contingent. So, far from being self-refuting, such a claim says: if no God then logical impossibility (ie, God cannot not exist). And, if anything, insisting that we cannot mean absolute nothing when we predicate anything of nothing supports that claim! What we can dismiss out of hand is your P1, and your P2, which doesn’t leave much for your conclusion (unless you’re arguing cutely that your conclusion comes from nothing).

Your “whac-a-mole twostep” is also flawed. Following the link to The Lame That Won’t Die I see that you think theists believe that God “just exists for no reason,” and no doubt this is your justification for allowing an always existing quantum vacuum in His stead (especially given empirical observations of quantum vacuum).

Two problems with this: 1. God doesn’t just exist for no reason, but as Existence Itself, is the reason for His own existence; 2. Anything self-existing must always exist which implies no changing (as change is a kind of be-coming) – quantum fluctuations tell us the quantum vacuum changes.

Aristotelian Thomists certainly don’t hold that nothing “exists”, nor that God could be anything other than eternal. We’d have no problem denying your P1; Thomas Aquinas held that we cannot prove whether the universe had a temporal beginning a la Big Bang. Your P2 is certainly not describing absolutely nothing. That you proceed as if “This can only mean that nothing whatever exists except anything whose non-existence is logically impossible” only leaves me wondering when you’ll approach the logical impossibility of the non-existence of Existence Itself?

vaughnbodie:In any case which theists deny that absolute nothing is logical impossibility?

Please point me to any statement by any theologian or apologist who argues that a state of absolutely nothing is in itself logically impossible.

(Arguing that “there is something now, therefore there cannot have been nothing then” is an empirical argument, not an argument from logical impossibility.)

I would be keen to know who does argue nothing is intrinsically impossible, and what arguments they use to that end.

(I am not asking for ontological arguments for God, per the following; rather, I am asking for arguments from the nature of nothing itself that nothing is impossible.)

Saying that out of nothing nothing is made does not affirm the actual existence of nothing.

You are clearly not following the argument. Read the very first paragraph of the post. I do not say theists affirm the existence of nothing (obviously, they affirm the existence of God, which is not nothing). I say they affirm that atheism entails there was nothing, and then they argue from that that atheism must be false because nothing cannot produce something (and something exists, ergo…). I then show that that inference is incorrect: if we affirm nothing, then something results. Therefore the theist’s premise that it wouldn’t is false.

Theists (at least Thomists) insist that God is logically necessary.

I know. Read paragraph 7 of the post.

And, if anything, insisting that we cannot mean absolute nothing when we predicate anything of nothing supports that claim!

No, it doesn’t. All it supports is the conclusion that logically necessary things will always have existed. For that to support the necessary existence of God requires that God be independently proved to be logically necessary. That has never been successfully done. As my post points out, with references.

What we can dismiss out of hand is your P1, and your P2, which doesn’t leave much for your conclusion (unless you’re arguing cutely that your conclusion comes from nothing).

I don’t see the logic of your tactic here. Theists accuse us of affirming P1. So what sense does it make for you to “dismiss it out of hand”? That only throws the argument to the atheists. If P1 is false, then the last paragraph of my post follows, and theism is then not supported. Remember, this post is about the theist’s argument summarized in paragraph 1. You have a hard time keeping your eye on the ball.

Following the link to The Lame That Won’t Die I see that you think theists believe that God “just exists for no reason,”…

No, I affirm that that is what theism entails. Theists (today) reject a contingent god, therefore retreat to a necessary god, but (as noted in this post) all attempts to prove such a thing have failed. That leaves no reason for God to exist. Therefore he just exists for no reason (if he exists).

Two problems with this: 1. God doesn’t just exist for no reason, but as Existence Itself, is the reason for His own existence; 2. Anything self-existing must always exist which implies no changing (as change is a kind of be-coming) – quantum fluctuations tell us the quantum vacuum changes.

Replace “God” with “quantum space” in the above sentences and statements (1) and (2) remain just as true. That’s the problem pointed out in the last paragraph of this post.

You are confusing the underlying facts (the properties of quantum space, which never change) with contingent results (the things quantum space causes to exist). If you applied that standard to God, then God also changes (because he causes things to exist that constantly change, too).

Of course, the Biblical God changes (he changed his mind about the covenants, for example, and is constantly changing his mind about when to start and stop punishing Israel, and changed his mind after the flood, and changed his mind after seeing that Adam was sad being alone in the garden, and changed his mind after Eve ate the apple, and so on). So I can only assume by (1) and (2) you are repudiating almost all sects of Christianity and declaring the entire Old Testament to be literally false, and also rejecting the trinity, because that would entail God changed by acquiring, and then losing, a body, and by living and dying, and so on, and also rejecting the concept of a new testament altogether (since if God never changes, then he can’t ever have once required us to live by Torah law and then later stopped requiring that of us). And so on. But that’s your problem. As for a quantum space, it appears to have a much stronger claim to never changing than God does (it’s hard to imagine even how a God who never changes could ever create something, since that requires a decision and an action, which are fluctuations, whereas a changeless, time-stopped person can’t think, much less decide or act).

Your P2 is certainly not describing absolutely nothing.

Yes, it is, by your own standards even: you just waxed on about how logically necessary things will always exist even when nothing else does. P2 simply affirms that principle (all it says against you is that it admits that no one has proved God to be one of those logically necessary things; but that is not against you, but is what is actually affirmed by the theists my post is arguing against: they say that if atheism is true then P1 is true, and that entails P2 is true…again, this is what theists are saying about atheism, not what I am saying about theism…get your eye back on the ball).

I’m afraid I couldn’t find a way to reply to your reply to my comment #25.

Carrier wrote:

”The principle of sufficient reason only says that something must have a reason to exist. If nothing necessarily becomes something, then that satisfies the principle of sufficient reason. Therefore the principle of sufficient reason can be true when ex nihilo nihil fit is false.”

All the work is done by “if nothing necessarily becomes something”. Yes, if nothing is really actually some thing(s), then that not-nothing satisfies the PSR. But if nothing is not-nothing you haven’t shown ex nihilo nihil fit to be false as, by your definition, we must mean “out of not-nothing not-nothing comes”.

In any case, that nothing means something is denied. And if by nothing we mean nothing? Then the PSR and ex nihilo nihil fit just are saying the same thing.

Look, ex nihilo nihil fit just is a weak version of the strong PSR that you stated. Rather than accusing me of being badly confused, perhaps you should first read The Atomists: Leucippus and Democritus – Fragments a text and commentary by C C W Taylor? Hell you could just follow your own Wikipedia link (I mean, you expected me to) to read the external links it gives to The Principle of Sufficient Reason: a reassessment by Alexander R. Pruss, and A Defense of a Principle of Sufficient Reason by famously atheist Quentin Smith. I think you’ll see the connection that eluded you before.

Thanks for your reply; I appreciate you giving my comment your time however, as a matter of self-awareness (to say nothing of manners), I’d say it’s fresh for a historian who is trying to argue that nothing really means the laws of logic, math, and probability, to accuse others of being badly confused!

vaughnbodie:All the work is done by “if nothing necessarily becomes something”. Yes, if nothing is really actually some thing(s), then that not-nothing satisfies the PSR. But if nothing is not-nothing you haven’t shown ex nihilo nihil fit to be false as, by your definition, we must mean “out of not-nothing not-nothing comes”.

And the latter kind of nothing is logically impossible, so it can’t ever have existed if atheism is true. Therefore a theist can never propose its existence as an argument against atheism.

vaughnbodie:Look, ex nihilo nihil fit just is a weak version of the strong PSR that you stated. Rather than accusing me of being badly confused, perhaps you should first read The Atomists: Leucippus and Democritus – Fragments a text and commentary by C C W Taylor? Hell you could just follow your own Wikipedia link (I mean, you expected me to) to read the external links it gives to The Principle of Sufficient Reason: a reassessment by Alexander R. Pruss, and A Defense of a Principle of Sufficient Reason by famously atheist Quentin Smith. I think you’ll see the connection that eluded you before.

Here’s what I think Jack is trying to say. The Principle of Sufficient Reason basically comes down to the following:

(PSR): X exists iff there is a reason justifying X’s existence.

This is supposed to be relevant to the discussion about absolute nothing, because in absolute nothing, nothing at all exists. If that is the case, then the following biconditional applies:

(~PSR): X does not exist iff there is no reason justifying X’s existence.

If (~PSR) is true, which is necessarily must be since it is simply the negation of (PSR), then in absolute nothing, there are no reasons applicable, because there is nothing existing in absolute nothing. And if there are no reasons, then there is no logic either, because logic counts as a reason. Thus, logic does not apply to absolute nothing.

dguller:Here’s what I think Jack is trying to say. The Principle of Sufficient Reason basically comes down to the following:(PSR): X exists iff there is a reason justifying X’s existence. This is supposed to be relevant to the discussion about absolute nothing, because in absolute nothing, nothing at all exists. If that is the case, then the following biconditional applies: (~PSR): X does not exist iff there is no reason justifying X’s existence. If (~PSR) is true, which is necessarily must be since it is simply the negation of (PSR), then in absolute nothing, there are no reasons applicable, because there is nothing existing in absolute nothing. And if there are no reasons, then there is no logic either, because logic counts as a reason. Thus, logic does not apply to absolute nothing.

Correct. But as I have explained several times now, this requires “absolutely nothing” to mean a logically impossible state of affairs. It is therefore irrelevant. It doesn’t apply to any kind of nothing that can ever have existed.

Since there are other kinds of absolutely nothing (and the most minimal kind that is logically possible is the kind I defined in my post), the PSR is not synonymous with ex nihilo nihil fit.

“Theists accuse us of affirming P1. […]Remember, this post is about the theist’s argument summarized in paragraph 1.”

Yes, but your P1 actually says: In the beginning there were only the laws of logic and probability.

Given that you haven’t actually adduced any theist who has said, in Latin or otherwise, that out of only the laws of logic and probability nothing comes, we can dismiss P1 out of hand. And as P2 is just what follows if P1 is true it doesn’t leave a whole lot for your conclusion unless this argument is a cute way of showing something coming out of nothing.

Look, if David Blaine told you “there is *nothing* up my sleeve except the entire apparatus necessary for the following trick,” you’d say, “That’s not nothing.” And you’d probably be unimpressed if he insisted that he’d just shown you something from *nothing* thus disproving the old adage.

And it is an adage. ex nihilo nihil fit is not a law. A law of what? It is, as I said before, merely a way of stating the PSR (a limited, and so weaker, version at that!) If the stronger version stated by you holds, the weaker version is entailed. And you say it holds.

vaughnbodie:Yes, but your P1 actually says: In the beginning there were only the laws of logic and probability.

Correct. That’s exactly what I said, in great detail, in the post itself.

Given that you haven’t actually adduced any theist who has said, in Latin or otherwise, that out of only the laws of logic and probability nothing comes, we can dismiss P1 out of hand.

You are hopelessly confused. Still. You clearly think I am arguing something else. Even though I explained your mistake upthread, you here reveal you still don’t even realize your mistake. This is a pointless conversation. Until you show that you understand what my argument is, there is no reason for you to continue attacking it. You are just boxing with shadows at this point.

ex nihilo nihil fit is not a law. A law of what? It is, as I said before, merely a way of stating the PSR (a limited, and so weaker, version at that!) If the stronger version stated by you holds, the weaker version is entailed. And you say it holds.

As I already explained, you clearly don’t understand what the PSR is or its historical or logical relation to ex nihilo nihil fit. And that despite the fact that I have corrected you on this. He who will not listen, cannot argue.

Linusvanpelt:[Re: ‘If the laws of logic don’t exist, then by definition that means logically impossible things can exist.’] I don’t see how anything can be logically impossible in the absence of any laws of logic?

You have two options: it is possible for logically impossible things to exist, or it is impossible for logically impossible things to exist. The latter entails P1 as I define it. The former entails all bets are off. Since then, no logical conclusion about what happens has any claim to being true, i.e. then “nothing” can become anything simply because no logical impossibility exists and therefore nothing is impossible–not anything whatever; and one cannot argue otherwise without circularly assuming that “nothing” obeys logic, which requires rejecting the premise that logically impossible things can happen, which lands you back at P1…there is thus no escape.

Of course, I think the idea that logically impossible things can exist is outright madness. It is not merely inconceivable, it’s beyond inconceivable. Hence I cannot fathom why anyone would believe it.

Thanks. My problem is that an absence of any logical rules (i.e. an absolute ‘Nothing’) wouldn’t entail the possibility of logically impossible things existing; it’d just mean there are no standards to define what’s logically possible and impossible in the first place. How do we get around this?

linusvanpelt:My problem is that an absence of any logical rules (i.e. an absolute ‘Nothing’) wouldn’t entail the possibility of logically impossible things existing; it’d just mean there are no standards to define what’s logically possible and impossible in the first place. How do we get around this?

You aren’t making any sense. “There are no standards to define what’s logically possible and impossible in the first place” is directly synonymous with “there is a possibility of logically impossible things existing.” These are not different statements. They state exactly the same thing.

By analogy, saying “there are no standards to define whether cats or dogs will come through my door” is directly synonymous with “cats or dogs can come through my door.”

In terms of set theory: we have one set (that of all logically possible things) and another set (that of all logically impossible things), which two sets exhaust the entire contents of a third set, that of all things whatever. If nothing determines which set’s contents will materialize, then either set’s contents can materialize. Therefore, logically impossible things can exist or occur.

That’s simply what you are saying when you say nothing determines what exists.

linusvanpelt:‘You have two options: it is possible for logically impossible things to exist, or it is impossible for logically impossible things to exist.’ I don’t see how we’d have either option if there were no laws of logic? What standard would distinguish logically possible from logically impossible?

It is not a standard, but the definition of the words we are using, and therefore what we are talking about. Anything that violates the law of non-contradiction is a logical impossibility. Thus to say that logical impossibilities can happen is to say that things can happen that violate the law of non-contradiction, i.e. directly contradictory states of affairs can exist or arise or occur.

Thus, if you were to say that “nothing” lacks even logic, you cannot argue “from nothing, comes nothing” because that would require “nothing” to obey logic, or else it would simply not be true, i.e. if there is no logical argument for “from nothing, comes nothing” then there is no reason to believe “from nothing, comes nothing” is true; whereas if there is a logical argument for “from nothing, comes nothing” then that argument would not apply when logic doesn’t apply and it therefore would again be false; either way “from nothing, comes nothing” is false.

This is my last substantial comment as apparently I’ve exhausted your goodwill. Thanks for the to-and-fro, though I’m afraid you are not persuasive.

Let me first summarize your argument in your own words so you can be sure I have not misunderstood, or wilfully mischaracterized, it:

[…] nothing is logically impossible, so it can’t ever have existed if atheism is true. Therefore a theist can never propose its existence as an argument against atheism.”

For a moment, let’s leave aside the fact that you are complaining about a straightforward counterfactual on the basis that the counterfactual makes obvious the logical impossibility of the conditional. We’ll come back to it.

Nothing, you argue, is a logical impossibility as the laws of logic are logically necessary, and cannot not exist. By the laws of logic, the logical necessity of the laws are the reason for their own existence. In one reply to me you put it thusly: ”The principle of sufficient reason only says that something must have a reason to exist. If nothing necessarily becomes something, then that satisfies the principle of sufficient reason.”

But here is your problem: the laws cannot be the reason for themselves because they must be before they can be a reason for themselves (or anything). Only being itself can be the reason of its own being; or to avoid confusion only existence itself can be the reason of its own existence. This does not mean the laws can’t always have existed; merely, they cannot be the reason for their own existence which leaves the question, “what is the reason for their existence?”

Well, that’s one of your problems. Apparently you’ve also convinced yourself that nothing really means (and has to mean) the laws of logic and probability along these lines:

P1: Laws of logic and probability are logically necessary
P2: The logically necessary is that which must exist
C1: The laws of logic and probability are that which must exist

But I argue:

P3: That which must exist is not nothing
C1: But the laws of logic and probability are that which must exist
C2: The laws of logic and probability are not nothing

Given that every premise and conclusion except P3 and C2 is yours, you must deny P3 and so C2, or you must stop banging on about how you’ve proved ex nihilo nihil fit false.

If the former, then rather than is not “that which must exist is nothing” which may be stated “that which must exist is logical impossibility”; and, by your ridiculous injunction against nothing that we ”can never propose its existence as an argument”, that can be dismissed with a wave of the hand.

Otherwise, ex nihilo nihil fit just is true as nihil must mean the laws of logic and probability and you have attempted to argue that the laws of logic and probability are the reason for their own existence.

How is the new translation “Out of the laws of logic come the laws of logic” not just a summary of your own argument for the laws’ self-existence?

vaughnbodie:In one reply to me you put it thusly: ”The principle of sufficient reason only says that something must have a reason to exist. If nothing necessarily becomes something, then that satisfies the principle of sufficient reason.” But here is your problem: the laws cannot be the reason for themselves because they must be before they can be a reason for themselves (or anything).

This is fallacious. You are presuming temporal order is necessary; it is not. If A must exist for B to exist, all we need is for A and B to simultaneously exist, we don’t need A, then B (or B, then A).

An example is that a triangle can only exist if lines exist. It is not as if I have to first make lines exist, wait around, and then make a triangle. The instant a triangle exists, lines exist.

So, too, the instant anything exists (even a state of nothing), logical necessity exists. It is not as if you have to have one, wait around, and then get the other.

This should be obvious to anyone familiar with ontological arguments, which presume to prove that God necessarily exists, therefore (by definition) there can’t ever have been a place or time where he does not exist. He simply always exists, even if nothing else exists. If it were possible for nothing to lack God, then God by definition is not logically necessary. Thus, all ontological arguments assume what I am assuming: that if something necessarily exits, by definition it can’t ever have not existed, therefore there can’t ever have been a state of nothing that lacked it. As for God, so for anything else that is logically necessary.

Only being itself can be the reason of its own being; or to avoid confusion only existence itself can be the reason of its own existence.

Prove it.

That is, produce a formal syllogism that demonstrates it.

Otherwise, this is just more fallacious argument from assertion.

P3: That which must exist is not nothing
C1: But the laws of logic and probability are that which must exist
C2: The laws of logic and probability are not nothing

This argument is irrelevant to my argument, because it uses a different definition of nothing. You are therefore committing a fallacy of equivocation (i.e. you can’t use C2 as a counter-example to P1 without an equivocation fallacy).

You might be attempting to play “language police” and insist that there cannot ever be different definitions of nothing, but that would be absurd in the face of all English language history and convention, so I have been assuming you weren’t arguing something so patently ridiculous.

By contrast, my analysis is: the theist says atheism must be false because if atheism is true, given the Big Bang Theory, there was once nothing, and nothing comes from nothing; I argue that either (a) “nothing” is logically impossible and therefore the theist’s second premise is false and therefore so is their conclusion unsound, or (b) “nothing” coincides with all logically necessary truths; if (a), the theist’s argument fails; if (b), the theist’s argument fails. And indeed on (b) not only does the theist’s argument fail, but it actually entails all the observed evidence of life and the universe to date (which is a startling conclusion, but nevertheless true).

This is fallacious. You are presuming temporal order is necessary; it is not. If A must exist for B to exist, all we need is for A and B to simultaneously exist, we don’t need A, then B (or B, then A).

I didn’t expect you to display a weakness in thinking common to philosophical dilettantes, who often confuse temporal priority with casual priority. The “before” in my claim referred to causal priority as my statement “this does not mean the laws cannot always have existed.” made plain. I’ll be more explicit in future.

Temporal priority has nothing to do with it. But being is ontologically prior to any causal power a thing might have. So to be the reason (ie, the cause) of their own existence, the laws of logic must be before they can be a reason. This is inescapable. And your example doesn’t describe the case here; you must prove how A can cause B to exist AND B cause A to exist. Neither can cause the other until the other causes it exists. Of course I’m sure you’ll dismiss vicious regress as facilely as you dismiss nothing. Until you can do that your argument fails so don’t worry about how being itself circumvents this problem.

The classic example: nothing can be temporally prior to something eternal. But an eternally existing footprint in the sand cannot be ontologically prior to the foot that’s causing it, even as the foot is not temporally prior to the footprint (on account of them both being eternal).

vaughnbodie:Being is ontologically prior to any causal power a thing might have. So to be the reason (ie, the cause) of their own existence, the laws of logic must be before they can be a reason.

I agree. You were talking about extensions of time, not the existence of logically necessary facts. By definition logically necessary things cannot not exist; therefore, if logically necessary things must exist at some time, then time is a logically necessary thing. We’ve been over this. There will therefore never be a non-existence of time. That does not entail an extension of time. If there is only one indivisible point of time (in any model thereof, corresponding to the zero on a timespace coordinate grid), then the laws of logic exist at that, and therefore precede all other things, including all extensions of time (i.e. all universes).

An eternally existing footprint in the sand cannot be ontologically prior to the foot that’s causing it, even as the foot is not temporally prior to the footprint (on account of them both being eternal).

Not ontologically prior, but they can be ontologically simultaneous. That’s the point.

William Lane Craig used a bowling ball on a pillow as an example: if both exist eternally, you do not need one to temporally precede the other. The bowling ball displaces the pillow eternally; there is never a location in time when it does not. Thus, there is no temporal order; there is therefore no ontological order, either: they always co-exist. There is nothing logically contradictory about that. Here, the laws of logic are the ball (more properly, the set of all logically necessary things is the ball), the singularity (a singular point of space-time that necessarily exists) the pillow, and all universes subsequent to that (all extended dimensions of time) are temporally and ontologically caused to exist by those.

Carrier: “You are therefore committing a fallacy of equivocation (i.e. you can’t use C2 as a counter-example to P1 without an equivocation fallacy).”

Sigh. Actually you are the one who is equivocating. You are the one who is using the same word “nothing” to mean both nothing, and “nothing but that which is logically necessary.” Use the latter if you wish, but use it consistently – ie, use your new definition in ex nihilo nihil fit too. I’ve pointed this out many times; explicitly in the argument I said if you have a problem with C2, you must deny premise P3 (as it’s the only one you haven’t argued for yourself) or use your new definition of nothing in ex nihilo nihil fit too. But as you say, “he who will not listen cannot argue.”

Simply – you’ve made a case that nothing cannot exist; fine, don’t then call whatever’s always existing by logical necessity nothing. Why would you do that? That’s equivocation. Just say “nothing never existed” and you won’t make such a disastrous mess.

Disastrous for atheism that is for what you are arguing is little different than the extreme realism of, say, Plato. His Third Realm may have been more fully stocked with ideas, but yours contains at least the laws of logic, the laws of probability, and Existence too (eventually you’ll see that you presuppose Existence if you actually argue NOTHING BUT logic and probability are always existing).

Necessarily existing Being/Existence, the order of logic and math – this is starting to sound familiar. Just like Plato’s Divine Third Realm the existence of your Must-Haves is more real than the rest of reality too (after all, they alone are logically necessary; they alone must exist). Hell we may as well write your name in the Classical Theists’ club book. It won’t be long before you argue that the simultaneous, eternal existence of all this nothing (ha!) is unified in one logical entity.

Actually you are the one who is equivocating. You are the one who is using the same word “nothing” to mean both nothing, and “nothing but that which is logically necessary.”

You evidently don’t know what an equivocation fallacy is. An equivocation fallacy occurs when you use a term to mean one thing at one point in an argument, and then another thing at another point in the same argument. Since in my argument I consistently always use exactly the same definition of nothing (the one I outline in the article), I am not committing any equivocation fallacy. My P1 argument is valid and sound.

Use the latter if you wish, but use it consistently – ie, use your new definition in ex nihilo nihil fit too.

I do. I first show that nothing without logically necessary things is logically impossible, therefore P1 by that definition can never be true (therefore the theist can never make an ex nihilo argument from that definition, since no such state will ever have existed, even if God does not exist). It necessarily follows that the only ex nihilo argument left for a theist to make against atheism is one that adheres to my definition of nothing (nothing + all logically necessary things). But on that definition, my P1 argument follows. And so the ex nihilo fails again.

Thus, all ex nihilo arguments fail either by asserting a premise that is logically impossible (and therefore false, therefore making that argument de facto unsound), or by asserting a premise that entails we would exist and observe a universe just like ours in all essentials (therefore making that argument invalid, because it fails to validly infer the contrary conclusion from its premise). Unsound or invalid. Either way it fails. That’s my argument.

Do you see how this works now?

His Third Realm may have been more fully stocked with ideas, but yours contains at least the laws of logic, the laws of probability, and Existence too (eventually you’ll see that you presuppose Existence if you actually argue NOTHING BUT logic and probability are always existing).

The difference is that nothing is a physical state, and logical “laws” are merely human descriptions of the physical fact that logically impossible things can’t exist or happen, which is a physical property of any absolute nothing-state (any such state, that is, whose existence is logically possible; no other nothing-states matter, since they can’t ever have existed). No Platonic forms are needed. All that exists is that which cannot not exist. Everything else is contingent, and therefore, in that state, not yet existent.

You still haven’t proven ex nihilo nihil fit false. You seem unclear on the ways in which a premise may contain conclusions.

If the proposition is universal the subject is distributed, or taken to its widest extension; but see that when you allow the sophistry of “nothing = (nothing but) certain laws (of probability and logic)” you make the proposition “ex nihilo nihil fit” particular, not universal. In this case the subject rather has full comprehension ie, it has all the notes comprehended in the predicate. So the revised ex nihilo just says “out of certain laws, certain laws come,” and is silent on anything beyond that. This may, or may not, be false. To me it seems an uninteresting circular truism, but given that you try to argue, and have subsequently defended, that certain laws are the reason for their own existence you certainly can’t deny it without contradicting yourself.

“So if that’s what theists mean by “if there was no God, then there was once absolutely nothing,” that not even logically necessary things existed, then their claim is self-refuting. We can then dismiss it out of hand.”

You are also unclear how a hypothetical syllogism works. The statement you quoted as something theists might mean is not self-refuting. Let’s look at this species of hypothetical more closely:

This conditional syllogism derives its force from an affirmed connection between a condition and a consequent; so that, if the condition is verified, the consequent must be admitted. Therefore, if the consequent does not exist, the condition is known not to be verified. Hence this argument may validly conclude in two ways:

1. Affirmatively: the condition being affirmed, the consequent must be affirmed; but not vice versa. Or,

2. Negatively: the consequent being denied, the condition must be denied; but not vice versa.

If you insist absolutely nothing is impossible, you have chosen the latter and denied the consequent. “If there was no God, then there was absolutely nothing” is not self-refuting and this is maybe clearer when it’s viewed as the hypothetical corollary of the categorical “Before Creation there was nothing but God.” If you think that by re-defining “nothing” you can affirm the consequent, well so what? This does not affirm the condition and the rest of your argument amounts to “if there was no God, then there was nothing but all the things that God is.” You just have the attributes wrong, and choke on the name.

“But if they allow that logically necessary things still exist even when there is otherwise nothing, then we have a “nothing exists” that is logically possible. There could have been such a state of being, of there once being nothing, in that sense.”

Why would they allow logical necessity without a ground for such necessity? Why would they allow anything logical absent a mind? Why, if necessary things must exist according to the atheist, should they allow themselves to suppose hypothetically that God, the one self-subsisting necessary being, does not exist? It’s all just wrong and internally inconsistent.

On your definition of “nothing,” such a state of nothing cannot exist (it’s logically impossible), therefore ex nihilo nihil fit is irrelevant even if true (since there can never be nihil, the matter of what comes of it is moot).

On any definition of “nothing” that is as close to your definition as is logically possible, but for which such a state of nothing can exist (it’s logically possible), ex nihilo nihil fit is false (as my main post’s argument proves).

Everything else you say above is irrelevant unless you can prove God’s existence is logically necessary.

No real criticism of your argument here but I had to respond to your suggestion that you had corrected me on the PSR and its logical or historical relation to ex nihilo nihil fit (and then I’m really done!)

Replying to my claim that ” The adage ex nihilo nihil fit is just a formulation of the principle of sufficient reason.” You said:

“That’s not true. The ex nihilo argument predates Christianity (it was developed by the Presocratics and taken up by later pagan philosophers). The principle of sufficient reason was independently developed by the presocratics. They were not connected then, and I am not aware of when they ever were. The principle of sufficient reason only says that something must have a reason to exist. If nothing necessarily becomes something, then that satisfies the principle of sufficient reason. Therefore the principle of sufficient reason can be true when ex nihilo nihil fit is false. They therefore cannot be the same thing. And historically they never have been.”

I pointed to a number of references that I said supported my claim, and you further replied:

None of those references contradict what I actually said.
Which would suggest you are the one who needs to read them.

Quoting from The Principle of Sufficient Reason: a reassessment:

“One of the central claims defended there will be that as soon as we accept even a relatively weak version of the principle [of sufficient reason], such as that ex nihilo nihil ﬁt (nothing comes from nothing), we should for the same reason accept the stronger one” (emphasis in original)
Or:
“The PSR ﬁrst shows itself clearly in Parmenides’ second argument against becoming. If something comes to be, it does so from something or from nothing. It is against this second possibility that the PSR is ranged. Parmenides asks: “[W]hat need would have driven it later rather than earlier, beginning from the nothing [tou medenos arxamenon ˆ ], to grow?” […] Thus, Parmenides employs the PSR to argue for the ex nihilo nihil principle.” (emphasis in original)

And there’s plenty more in that vein. CCW Taylor’s work on the Atomists of course recalls similar argument by Democritus using an ex nihilo formulation of the principle to ask why a contingent thing should appear at the time it does and no other.

You were unnecessarily snide in your remarks regarding my understanding of the PSR. One of us may be confused, ignorant, or dishonest about whether the PSR and ex nihilo nihil fit are related but it isn’t me.

vaughnbodie: None of which contradicts what I actually said. You did not say “they are closely related,” nor did I say they were not linked in 20th century philosophy (I said only that I did not know of when they were ever linked).

If ex nihilo is a way of stating the PSR then your argument is self-contradicting (on more than one point). Whether you know it or not, the principle of sufficient reason *is* “closely related, if not fully identical, to the principle “ex nihilo, nihil fit”“. And by “closely related” is meant that ex nihilo nihil fit may be less general than the formally expressed PSR but is a formulation (ie, expression, or statement) of the principle. If you choose to gloss over the fact that many authorities would deem them “fully identical” it still cannot help you to accept the strongest (ie, most general) version of the principle as that entails any less general version of it. And accept it you do; so, at the same time you claim that one and the same principle is logically necessary in its most general expression, but “demonstrably false” when expressed (less generally!) as ex nihilo.

Perhaps you should be explicit and tell us if you deny that ex nihilo is a (less general) statement of the principle of sufficient reason? Forget all the bluff about the principle’s genesis or its standing in the 20th century (?? how is this relevant?) as this just obscures the point. Do you deny that ex nihilo is a (less general) statement of the principle of sufficient reason?

But even this glaring inconsistency is as nothing compared to how you contradict yourself when your argument depends on (and asserts) the following absurdity: nothing is not nothing. In fact, given that the principle of contradiction rises immediately from apprehending the opposition of being to non-being, I’d say there is no more textbook violation of that First Principle.

Once you’ve concluded nothing is impossible there is no justification (zero, zip) to pick up the word and redeploy it. That some things are logically necessary and/or eternally existing doesn’t justify terming these things “the only state of nothing that is logically possible.” There are plenty of words other than “nothing” that you could choose to describe “nothing but necessarily existing [whatever].” If you were sufficiently motivated to make your argument transparent and accurate this would be plain to you. It should be enough to point out the absurdity of nothing is not-nothing but why do you continue using the word “nothing” to describe not-nothing? Well, clearly:

a) you’re trying to upturn ex nihilo nihil fit by proving it false even as you insist stronger versions (expressions, formulations) of the PSR are necessarily true. But, more interestingly,

b) as soon as we drop this “not-nothing is nothing” spiel, we see that you are making a fair approximation at a theist’s argument for God. You’re still mistaken in details, inconsistent, and loose in your definitions otherwise you’d have concluded attributes such as Intellect must go along with Necessarily Existing, Eternal, and Self-Subsisting but, as I say, this is still pretty far away from an Atheist victory. Avoid “God”, if you must; call the necessarily existing ground of all being, “Agent Zero”, “the Boot Sector”, “The Carrier-Alpha”, or anything else suitably scientific sounding and you have a rose by any other name.

Because when you really get down to it you’re agreeing with the theist’s declaration that “Before Creation there was nothing but God.” The unavoidablecorollary to that is, if there is no God (ie, atheism is true) then there was nothing. When your very first sentence in defence of the argument is “No, the word “nothing” in P1 is defined in that post as being nothing butthe existence of logically necessary things” it’s safe to say you’re arguing over a name and some attributes. Which is a big deal for nerds like me, but is not much of a victory for the anti-God project.

But even this glaring inconsistency is as nothing compared to how you contradict yourself when your argument depends on (and asserts) the following absurdity: nothing is not nothing.

That is not an absurdity when you recognize that there are many different kinds of nothing. If there is nothing in my garage, there is actually air in there, some spiders, radio waves and cosmic rays passing through it, a sea of virtual particles at the subatomic level, etc. You would not say it’s “absurd” to say there is nothing in my garage when it’s empty. Or “nothing” in your pockets. Etc. Most uses of the word “nothing” are not nothing in some sense or other, because there is always something there.

Thus the only relevant issue here is what is the most nothing nothingness that can logically exist. The rest of my argument follows.

Your continuing to ignore every single element of my argument notwithstanding.

Regarding a previous offlist objection, more can be said, on three stages of analysis, to clarify why my conclusion follows. First epistemological, second physical, third metaphysical. I was asked offlist again to prove this, so here goes…

The basic objection is “what if the probability distribution for all possible multiverses is not even but skewed, e.g. some outcomes being more probable than others, for no reason.” In other words, it’s a brute fact objection, whereby the “brute fact” being proposed is that there just might be some other probability distribution as a mere “brute fact.” It is this “brute fact” that I am saying would constitute “something” (a property) and therefore will not exist on P1.

Thus, to assert this brute fact is in effect to deny P1 (which I accept as a possibility, one that I discuss at the end of the original post). It is not a valid objection to P2 (or to C1 following from P2), because on P1, no such brute facts exist. Unless they are logically necessary, but then they would not be brute facts; and then you would have to prove the logical necessity of a non-even probability distribution for this objection to be applicable. Absent that, P2 is true, and C1 follows.

That’s the short answer. For those who need to see it worked out, here is the complete answer:

Epistemologically: claiming an uneven distribution might have obtained doesn’t get you anywhere because there are infinitely many ways to distribute the probabilities unevenly, and each of those schemes is then as likely as every other.

For example, if I have a six-sided die, and we don’t know if it’s rigged or not and can’t test it, you can say there is “maybe” a 100% chance it will always roll a 6, or a 30% chance of one number, and 20% of another, and so on. But there are infinitely many possible distributions you can describe as to what the odds are on this die. When you average for them all, you get an equal probability for every number (this is actually a basic principle in statistics that all science is now built on: see William Faris, Notices of the American Mathematical Society 53.1 [January 2006]: 33-42). Exactly the same as a non-rigged die. You therefore need a reason to believe one of those schemes is more likely than another. If nothing exists to decide that, then you can’t arbitrarily claim one is true and the others are false.

In other words, each possible scheme is another distribution, each no more probable than the next. It is thus governed by the inevitability that any one of those schemes could happen, and nothing decides which it is. So when there is nothing to make any one of them more likely than any other, they are all equally likely. If you then claim that that distribution might be uneven (and thus not every scheme is equally likely), then the same goes again: there are infinitely many schemes for that as well, and when we average them all, we end up where we started. It’s infinite regress. But you always end up in the same place: each possible outcome has the same probability as every other. And that always translates back down the line to each configuration of universes has the same probability as every other. Even if other probability distributions are possible.

Physically: even if this decision among all possible probability distribution schemes actually occurs somehow, since “deciding” among all these schemes of probability distribution is also done at random, the net effect is physically the same as just described, e.g. if there is a skewed scheme whereby there is a 90% chance of only one universe, this scheme will itself be extremely improbable, there being many more schemes in which that probability is vastly less; and which scheme obtains is random, so the net probability of there being only one universe remains lower than that of any greater number of universes, even if there is a skewed probability distribution, precisely because nothing makes any one skewed scheme more likely than another. Again, trying to avoid this by inventing a “hyper scheme” of a skewed probability distribution for all skewed probability distributions (of all possible configurations of universes), makes no difference. The same math comes down the line. And so on, no matter how many hyper-hyper-hyper schemes you propose.

Metaphysically: this objection doesn’t work anyway, because it violates the principle of sufficient reason: if there is nothing (I mean nothing) that makes one distribution more likely than another, then there can be nothing that does so (by definition), and therefore nothing does so, and therefore that distribution does not obtain.

The objector wants there to be some randomly chosen distribution, dictated neither by logic nor by any cause or anything whatever, but that is illogical. It requires imagining some “thing” wherein or whereby the “distribution” is decided before any selection is made using that distribution. That’s the “magical randomizer” I was talking about. You have to believe that something exists that chooses among the possible distributions and/or fixes it as one distribution rather than another. But when absolutely nothing exists, neither does that (whatever it would be). If instead you say that the distribution scheme is not fixed by any thing, but is chosen at random (as would have to be the case when nothing exists to determine which scheme will exist), then you are back to the statistical argument above, which ends up in the same place (physically and epistemically).

There is no getting around this.

In summary: if some non-even probability distribution existed, then that entails a selection was made among all logically possible distributions. That selection was not logically necessary. Therefore, when “nothing exists except that which is logically necessary,” that selection did not exist, either. By definition. Thus, we must exclude it. Otherwise, that selection would have to be a “brute fact” added onto the existence of nothing. Which is no longer nothing, but “nothing” plus one arbitrary brute fact. This therefore amounts to denying that a state of nothing existed, which means denying P1. Which again is fine; that’s simply not an objection to the validity of my argument, which already accepts and treats both possible outcomes (in which P1 is true, and in which P1 is false).

Another argument was provided offlist, which is an attempt at a reductio ad absurdum, only it is not valid (it does not demonstrate a logical contradiction and therefore is not a proper reductio ad absurdum but in fact a fallacious reductio ad ridiculum, which distinction I treated in another case already upthread).

This new argument can be summarized as “a lone blind caveman never moves from where he sits; he observes that the size of his cave can be any of infinitely many sizes; given P2, all are equally likely; therefore he would conclude that he can be certain his cave is infinitely large; that is absurd, therefore P2 is absurd and therefore to be rejected.”

This commits several fallacies. For one thing, this caveman’s certainty would be dependent on how certain he is that P2 is true, but it only is if P1 is true. This argument thus confuses our certainty whether P1 is true, with our certainty as to what is true if P1 is true, which is P2. For another thing, P2 is only true if P1 is true, and P1 asserts nothing exists, which means there cannot be a cave, much less a caveman. The argument thus operates on a false analogy. And third, the argument does not even validly show that P2 is false, without presupposing an infinitely large cave is false; if it is not false, then the argument does not argue against P2. This argument therefore confuses that which is counter-intuitive, with that which is false or impossible.

This objection is therefore multiply fallacious.

(1) It is an argument from the nature of existing things, not from the nature of absolutely nothing. What, for example, prevents the cave from being infinitely large? You have to presume knowledge of the universe and its contents, such as the size of planets and caves, to conclude that it is unlikely to be. But that’s not nothing. P2 does not follow if P1 is false. So any argument that presumes P1 is false (as the proposition “a universe exists with caves whose size is limited by physics” entails) cannot conclude that P2 is false when P1 is true. That would be a classic case of denying the antecedent (If P1, then P2; ~P1; therefore ~P2). What we want to know is if P2 is true when P1 is true. This objection, by requiring P1 to be false, has nothing to say about that.

(2) We are actually in this situation: we are the blind caveman. We can only see to a horizon of nearly 14 billion lightyears, but in fact we have no knowledge of the size of the universe. We know space-time is flat, which means theoretically it is infinite in diameter and content (since it is not curved in on itself and there is no logical way for space to “end” without more space existing beyond it, as famously demonstrated by Lucretius two thousand years ago). Like the blind caveman, we cannot see how large our universe is. And there is nothing we know of that would limit what size it is. So isn’t it therefore likely that it is infinite?

An analogous form of my argument actually proceeds here, and correctly, to show that indeed we can be highly certain that the universe is infinitely large…unless we discover something (some thing) that prevents that being the case. And that is the only relevant issue: whether there is some “thing” that changes what follows from current observations. And that pertains to whether P1 is true, not to what follows from P1. This objection is therefore confusing the two. There is nothing absurd about our universe being infinitely large. It may very well be. And the only thing that would stop it being so is some thing that prevents it being so. Which cannot exist on P1, and therefore this objection commits the fallacy of false analogy.

Just imagine trying to argue that the universe is only 16 billion lightyears wide and not larger, or a trillion-trillion lightyears wide and not larger, or any finite size D and not larger. How would you maintain that it is not larger? Based on what? Pick any size. On what basis would you argue our universe is probably not larger? Now assume you can find a “what” to base that argument on. What happens when that “what” doesn’t exist? That’s the situation entailed by P1.

The analogous premise would be P1*: “nothing limits how large our universe is” (and analogously, P1**: “nothing limits how large the caveman’s cave is”). If P1* is true (again: if it is true) then wouldn’t it follow that our universe is some infinite size? Yes, it would. You could only deny it by denying P1*. Likewise P1**. Thus, it is obvious that the “absurdity” that is attempted by this objection is not in fact absurd, but actually what necessarily follows from the premise P1. If that which is logically necessary sounds “absurd” to you, then the problem is with you, not logic. Because that which is logically necessary always trumps your astonishment. When you have to choose between which is correct, you must choose that which is logically necessary. Your intuition in that case is simply just wrong.

Even in our actual case (where we are not staring at nothing, but an actual existent universe), concluding the universe is very probably infinitely large is not absurd; and concluding it necessarily is infinitely large if nothing exists to limit its size, is not only not absurd, it’s logically certain. The only argument against the conclusion in fact is that there might be some as-yet-undiscovered “thing” that limits our universe’s size. Which is no longer a context of “nothing.” And therefore we’re back to either a false analogy, or a confusion between denying P1 (“because we might discover some thing always existed that instead dictated what happened”) and denying that P2 follows from P1.

(3) Finally, this objection confuses two different stages of scientific assertion. Scientifically speaking, P1 might be false (and the probability that it is false won’t be infinity to one against, an important distinction: my syllogism says nothing about the probability that P1 is true, it only says what else is probable if P1 is true). If P1 is false there may be only one universe or some finite number of them (that’s exactly what I said already in the original post). But what I am doing is deducing from the hypothesis that P1 is true (I am not asserting that P1 is true), which is what scientists do when they deduce from a hypothesis what will be observed and then go see what is observed.

Anyone using the “caveman argument” is getting this backwards, assuming that scientists can’t deduce from hypotheses what will be observed, because they haven’t observed it yet. That’s the opposite of how science works. The correct order is: you deduce first, then observe. Thus obviously we have to be able to deduce what will be observed before we can observe it. That’s what makes hypotheses testable at all. And in this case the hypothesis is P1, from which we can deduce everything my argument shows. That is what will necessarily be observed if P1 is true. The question then is, is that what we observe? As of yet, we cannot tell, because all we can see is this one universe. So the truth of P1 cannot be determined, at least not to a very high certainty. Which is essentially what the caveman argument is trying to say. But insofar as that is all it says, it is not a valid objection to what I actually argue, which is not that we know P1 is true, but that P1 would entail what we have so far observed. Many other hypotheses will likewise entail that. Therefore we need more evidence to determine which hypothesis is more likely (be it P1 or something else).

Thanks for the replies, Richard, and for being so generous with your time. It’s great to see the level of interaction you have with your readers. The argument is quite a feast and I’m afraid I’m chomping through it much slower than your other commenters.

My difficulties are much more basic than the objections raised elsewhere. I’m still at the very early stage of trying to pin down how we can rule out the possibility that ‘nothing exists’ entails ‘no laws of logic exist.’

I’m stumbling at the answer ‘Because that would mean logically impossible things can exist’. If no laws of logic exist, the category ‘logically impossible’ doesn’t exist either. It’s meaningless in the absence of laws of logic. I don’t understand how we can say ‘Because that would mean logically impossible things can exist’ when we’re imagining a lack of the very standards that could make things logically impossible in the first place.

Sorry to harp on about this – the discussion thread has moved way past this basic point and I’m sure I can get my head around it in my own time!

linusvanpelt:I’m still at the very early stage of trying to pin down how we can rule out the possibility that ‘nothing exists’ entails ‘no laws of logic exist.’

Why do you want to, though?

That is, why is it important to attempt to ascertain whether there is a definition of nothing, in which nothing can exist, and no logic governs what happens to it?

You seem to want a situation whereby there are two separate things: nothing, and the fact that logically impossible things can’t happen to it, as if the latter has to be added to the former by some mysterious force. That makes no sense. If “nothing” can have that property taken away from it, then it would follow that logic no longer governs how “nothing” will behave. By definition. In other words, that is what it means to take that property away. I have already discussed the consequences of this reasoning upthread.

Everyone else sees that you can’t take that property away from anything, not even nothing. Because then logically impossible things can happen. But logically impossible things are simply impossible. They can’t ever happen. And it’s insane to think they could.

I’m stumbling at the answer ‘Because that would mean logically impossible things can exist’. If no laws of logic exist, the category ‘logically impossible’ doesn’t exist either.

This is precisely the problem: if “the category ‘logically impossible’ doesn’t exist,” then nothing is logically impossible, which means everything is possible, even the logically impossible. Thus, you are actually arguing that “nothing” would be even more pluripotent than my P1 entails. I at least say that what can happen to nothing is restricted by logic. You are saying it is not even restricted by that.

I don’t, necessarily! But I’m just following the line of your own argument, to arrive at your formulation of P1 including the caveat about logically necessary things:

‘One might object at this point by asking how the laws of logic can “exist” when nothing exists… But…if the laws of logic don’t exist, then by definition that means logically impossible things can exist.’

What’s puzzling me is: logically impossible according to what standard?

linusvanpelt:What’s puzzling me is: logically impossible according to what standard?

That’s a meaningless question. We aren’t talking about “standards.” You seem to be confusing human language with reality. It does not matter what we call an apple, apples still exist and have the properties they do. Thus what our “standard” is for naming an apple is not relevant to the question of what properties apples have, or whether they exist.

Here instead of apples, we are talking about the set of all things, which can be split without remainder into two sets, those that are contradictory and those that aren’t. The only question is: can anything in the first set ever exist? That’s it. That’s all we are asking. If the answer is yes, then that amounts to saying “logically impossible things can exist.” This is true by virtue of human language (the one is literally identical in meaning to the other). If the answer is no, then that amounts to saying “logically impossible things cannot exist.” Again, this is true by virtue of human language (the one is literally identical in meaning to the other).

It will do no good to say “but human language didn’t exist” because that would be identical to saying that apples didn’t exist before human language existed. We are not talking about the language. We are talking about what the language refers to. Which is true or false regardless of what language we use and regardless if language exists or not. Thus, whether “things from either set can exist,” or “only things from the second set can exist,” is true or false regardless of the existence of any language to describe the difference.

Sorry, I’ll rephrase – logically impossible according to what? What would make a ‘thing’ ‘logically impossible’ if there were no laws of logic?

My whole issue is with ‘…if the laws of logic don’t exist, then by definition that means logically impossible things can exist.’

Logically impossible things couldn’t exist if there were no laws of logic – because ‘logically impossible’ just means ‘impossible according to the laws of logic’. If there were no laws of logic, there would be no laws to rule anything out as logically impossible.

This doesn’t entail ‘Then everything is logically possible.’ ‘Logically possible’ just means ‘possible according to the laws of logic.’ No laws of logic, no logical possibilities.

And that’s my question: what, in the absence of laws of logic, would rule anything out as logically impossible, or make anything count as logically possible?

‘You seem to want a situation whereby there are two separate things: nothing, and the fact that logically impossible things can’t happen to it, as if the latter has to be added to the former by some mysterious force.’

No, that’s not it – I’m still at ‘…if the laws of logic don’t exist…’ I’m saying that if the laws of logic don’t exist, it’s simply meaningless to talk about logically impossible things. For that matter, it seems meaningless to me to talk about ‘nothing’ as an ‘it’ to which things can happen, for reasons I’ll give below.

‘You seem to be confusing human language with reality.’

I’m not sure how I could possibly be doing this, given that we are presently using human language to investigate a hypothetical absence of anything we might associate with reality (including properties – again, see below).

‘We are talking about what the language refers to.’

But at this point we’re talking about ‘nothing’ and ‘…if the laws of logic don’t exist’. And I’m still just looking at whether one sentence is internally coherent. The one thing that seems certain here is that if there are no laws of logic, there are, by definition, no logical possibilities.

Nor, in the absence of laws of logic, would ‘nothing’ have any properties whatsoever, as far as I can see.

You’ve said (to Dguller) that nothing has the property of ‘remaining’ nothing – but in the absence of time, there is no ‘remaining’. Nor does it make sense to say that ‘nothing’ follows the pattern of ‘not doing anything’ – there’s nothing there to do/not do anything. This looks like a misuse of language. It implies the following definition of ‘nothing exists':

A) ‘Nothing exists’ means: there is a state of nothingness and it exists

But if a theist insists on the following definition:

B) ‘Nothing exists’ means: it is not the case that anything exists

…then it makes no sense to talk about nothing ‘doing nothing’ or ‘remaining nothing’. There is nothing to attach any predicates to. Incidentally, A) looks… like Anselmian sleight of hand. What I want is to block B).

‘…we are talking about the set of all things, which can be split without remainder into two sets, those that are contradictory and those that aren’t.’

If there is nothing, there is no ‘all things’. And if there are no laws of logic, there are no laws that would split these things (which don’t exist!) into two sets. We haven’t yet established the existence of any possibilities, because at this point we’re imagining an absence of any laws that would make anything count as (logically) possible. Nor are there properties, as we can’t ascribe properties to nothing without erroneously positing ‘nothing’ as an existing ‘something’ that persists through time, a move the theist can block by adopting definition B) above.

‘The only question is: can anything in the first set ever exist? That’s it.’

‘If the laws of logic don’t exist…’ – then there are no sets.

I’m fine with the idea that the laws of logic have to exist. And I think that your metaphysical naturalism (as far as I can tell) establishes it independently of this argument, so the rest follows. But I’m arguing with a couple of people over this post and I can’t for the life of me show them that ‘…if the laws of logic don’t exist, then by definition that means logically impossible things can exist’ isn’t self-defeating purely on its own terms.

I’ve already answered all these questions (some of them, several times). So you’re just talking in circles at this point. You’re clearly just not understanding me. So let me try a completely different tack.

Suppose we simply ask this question: “What will happen if there is absolutely nothing?” The ex nihilo argument against atheism declares the answer to be “Only nothing will happen.” Let’s call this proposition N.

How do we know that N is true?

(1) We can’t know it empirically, because we have made no observations of what happens to these nothings. So we have no evidence that “nothing happens” when there is “absolutely nothing.” So we can’t claim this is an empirical hypothesis. (Indeed, it would be logically impossible to empirically observe what happens to absolutely nothing, since that would require there to be something: an observer; but if there is an observer, there is not absolutely nothing. Unless, given my definition of nothing, observers are logically necessary beings, but I have never seen any valid argument that they are.)

(2) So you can’t claim that. So what then? We can claim N is logically necessary, i.e. that it is necessarily the case that any “absolute nothing” will only produce nothing. But you can’t claim that, because you are saying if nothing exists, neither does logical necessity. If there is no logical necessity, then there can be no logical necessity that “absolutely nothing” will only produce “nothing.”

(3) So you can’t claim that. What’s left? You only have one remaining option: admit that nothing obeys all logical necessities (i.e. that this nothing can never do something that’s logically impossible, and will always do what is logically necessary for such a nothing to do). But that entails my entire P1 argument. Because now, nothing obeys logic.

You obviously can’t appeal to (1). That leaves you stuck on the horns of a dilemma: you either assert (2), or you assert (3). If you assert (3), you have just conceded everything I have here said. So all you can do is assert (2). But (2) is a contradictory assertion: you, here and now, are asserting a logical impossibility, that nothing obeys logical necessity and does not obey logical necessity. This is not a property of the nothing, this is a property of your assertion, here and now. That is, you are contradicting logic, not the nothing. It simply makes no sense for you to declare “nothing obeys logical necessity and does not obey logical necessity.” So your argument that it does is simply false.

That means either nothing obeys logical necessity, or it doesn’t. If it doesn’t, then the ex nihilo argument fails (because N is then false, or not known to be true). If it does, then the ex nihilo argument fails (because of my P1 argument). Either way, the ex nihilo argument fails.

That’s my argument.

Now, in my article, I dismissed the approach of insisting this nothing doesn’t even obey logic, as being insane even to suggest (since it entails believing that logically impossible things can happen or occur, which is lunacy). But we could, if we wanted, develop a P1 argument that epistemically comes to the same conclusion, from the premise that “absolutely nothing” means a state of nothing that will obey no logic. Metaphysically, we could not know what would happen because no logic governs what will. But epistemically, because no logic governs what happens, all possibilities are equally likely (again, epistemically, to us; even if not in actual physical fact, which we won’t know, since the actual probabilities will be illogical). The same conclusion then follows, i.e. the epistemic probability that we would observe our universe is the same: infinitely near 100%, because we know of nothing that would make its probability otherwise (not even logical necessity could do so, because what will have happened to that initial state of nothing won’t even be governed by any logical necessity).

I think there’s a problem here: for something to happen, there must a time dimension for it to happen in. And time is a physical notion. Absolute nothing would mean no time or space, and so no possibility for anything to happen.

Many thanks – for some reason my last comment and your reply didn’t appear on the blog itself.

You say: ‘You aren’t making any sense. “There are no standards to define what’s logically possible and impossible in the first place” is directly synonymous with “there is a possibility of logically impossible things existing.” These are not different statements. They state exactly the same thing.’

Surely they state exactly opposite things?

The very reason why there’d be no logical laws under P1 is because there is nothing – no things exist. Under P1, ‘there would be no standards to define what’s logically possible and impossible in the first place… because nothing exists’.

Not only is this not directly synonymous with ‘There is a possibility of logically impossible things existing’ – the two statements contradict each other. To the extent that a ‘possibility’ is something, P1 rules it out. To the extent that a possibility can be said to exist, P1 rules it out. So P1 rules out ‘there is a possibility’. So if nothing exists, no possibilities exist by definition.

Instead, ‘Under P1 there would be no standards to define what’s logically possible and impossible in the first place… because nothing exists’ is directly synonymous with, ‘Under P1 there is no possibility of logically impossible things existing… because a possibility is something, and if there is nothing (P1), it is not the case that something exists.’

You say: ‘By analogy, saying “there are no standards to define whether cats or dogs will come through my door” is directly synonymous with “cats or dogs can come through my door.”’

Again, the very reason there are no standards (laws) concerning cats or dogs under P1 (‘Absolutely nothing exists’) is that if there’s nothing, there are no cats, dogs or doors, or anything else. That’s the whole point. If we flesh out the two statements with this in mind, we can see how they aren’t synonymous:

1) There are no cats, dogs or doors, so nothing exists that could be described as ‘a law defining the parameters of whether it is possible for cats or dogs to come through my door’.
2) Cats or dogs can come through my door (or any other possibility you want to allege of cats and dogs).

The easiest way to see that the two statements aren’t synonymous is to fit them into P1:

1) In the beginning, nothing whatsoever existed, and therefore there were no cats, dogs or doors, so nothing existed that could now be described as ‘a law defining the parameters of whether it is possible for cats or dogs to come through my door’.
2) In the beginning, nothing whatsoever existed, and therefore cats or dogs could possibly come through my door.

1 at least makes sense. 2 looks trippy. At the very least, the two aren’t synonymous.

linusvanpelt: The very reason why there’d be no logical laws under P1 is because there is nothing – no things exist.

And to say “there are no logical laws” is literally identical to saying “logically impossible things can happen or exist.”

These are not antonyms, but synonyms. The second sentence is a direct translation of the meaning of the first sentence.

As to the rest, you should attend to what I actually say in the original post. I quote it here:

All I will assume is what is undeniably true: that all the fundamental propositions of logic and mathematics are necessarily true (for example, all valid and sound theorems and syllogisms are necessarily true, in the sense that, when given their premises, their conclusions cannot be false; but not in the sense that their premises are necessarily true, even if they might be), and therefore there can never have been a state of being in which they were false.

Thus, I am not saying there were cats, dogs, etc., but that, even when there aren’t cats, dogs, etc., it is still true that if there were cats, dogs, etc., then (etc.). Do you see the difference? It cannot be that when cats don’t exist, that the statement “if cats exist, then {all true statements about cats}” is false. Likewise, it cannot be the case that when nothing has happened, that the statement “both x and ~x can happen simultaneously” is false.

In other words, what happens when there is nothing must still obey logic. Otherwise, it won’t obey logic. That’s what it means to say that it won’t obey logic. Those are synonymous statements. If there is that which does not obey logic, then all propositions of the form “both x and ~x can happen simultaneously” are false. That means anything can happen (literally: even logically impossible things, like “both x and ~x happen simultaneously”).

P3 is a statement that is necessarily true: “of all the logically possible things that can happen” (full stop; there being no other limits on what can happen but what is logically possible) “continuing to be nothing is one thing” i.e. one logically possible thing, “one universe popping into existence is another thing,” i.e. one logically possible thing, “two universes popping into existence is yet another thing,” i.e. one logically possible thing, “infinitely many universes popping into existence” is also one logically possible thing, and so on.http://freethoughtblogs.com/carrier/wp-admin/edit-comments.php?comment_status=moderated#comments-form
(Including “all configurations,” e.g. one universe popping into existence is technically not one thing but already infinitely many, since there are infinitely many universes that that one universe can be; and two universes is infinity times infinity many things, the same way if there are two possible universes, then one universe would be two possible things, and two universes would be four possible things, since you can have two #1’s or two #2’s or a #1-#2 or a #2-#1; etc. I discuss configuration counting in the following text.).

Since it would be logically impossible for this not to be true, P3 is necessarily true.

1. “There was once nothing.” – This statement is illogical, since there cannot be a time when nothing exists, or, particularly, when the spacetime system doesn’t exist. There cannot be any pre-spacetime times (I don’t mean only our spacetime bubble or island but spacetime as a whole). It is equally illogical to say that before something came into existence, there was nothing.

3. “Nothing” in the sense of “absolutely nothing” means “neither anything concrete (mental or physical) nor anything abstract”. But this can be split into three different questions:
i. Is it possible that nothing exists?
ii. Is it possible that nothing concrete exists?
iii. Is it possible that nothing abstract exists?

4. “All I will assume is what is undeniably true: that all the fundamental propositions of logic and mathematics are necessarily true (for example, all valid and sound theorems and syllogisms are necessarily true, in the sense that, when given their premises, their conclusions cannot be false; but not in the sense that their premises are necessarily true, even if they might be), and therefore there can never have been a state of being in which they were false.” – R. Carrier

The absence of being is not a state of being. And if there is nothing, there aren’t any propositions either. The necessary truth of a proposition is one thing, and its necessary existence another. A necessarily true proposition is such that if it exists, it must be true. But in case it doesn’t exist, it doesn’t have any truth-value, since nonexistent things don’t have any properties.

There are logically possible worlds which are truthless because they are proposition-/statement-/sentenceless. (Note that truthlessness is not the same as factlessness.)

Logically necessary truths are logically contingent entities.
Anyway, you’re begging the question against those who deny the existence of propositions as abstract entities, particularly as timelessly eternal ones that are both mind- and spacetime-independent.

The proposition “Nothing exists” is logically necessarily false, since if it were true, it would exist; and if it exists, it is not the case that nothing exists. Only the qualified proposition “Nothing concrete exists” isn’t logically necessarily false, since if propositions exist, they are arguably abstract entities.

5. “When nothing actually exists, all potentials exist.” – R. Carrier

I think this is false, because there can be no pure potentialities or mere possibilities, i.e. ones that aren’t potentialities or possibilities of any actualities. There inhere no potentials or powers in nothingness. Nothingness is and has nothing—end of story!

6. “I have argued that that which exists at no location or at no point in time, by definition exists never and nowhere, which is by definition not existing.” R. Carrier

This begs the question against the platonists, according to whom there are non- or extraspatiotemporal abstracta. Do you really want to define abstract objects away rather than argue metaphysically against them? This would be too cheap a victory, wouldn’t it?

“It is an open question whether everything that exists has some sort of spatiotemporal location. The empty set, and the pure sets generally, are supposed to be unlocated; if so, maybe that is bad news for the pure sets, or maybe it is bad news instead for the thesis that everything is located.
(I myself would deny that unlocated things are part of this possible world, or any other; but that is irrelevant, since I do not claim that everything there is must be part of some or another world. The pure sets might perhaps be a counterexample.)”

1. “There was once nothing.” – This statement is illogical, since there cannot be a time when nothing exists, or, particularly, when the spacetime system doesn’t exist. There cannot be any pre-spacetime times (I don’t mean only our spacetime bubble or island but spacetime as a whole). It is equally illogical to say that before something came into existence, there was nothing.

This is either an unintelligible statement or a logically contradictory statement. Either way, moot.

3. “Nothing” in the sense of “absolutely nothing” means “neither anything concrete (mental or physical) nor anything abstract”. But this can be split into three different questions…

Okay. So?

4. … The absence of being is not a state of being.

If that were true, then a state of nothing cannot exist (there can never “be” nothing if nothing is not a state of “being”). I already address this possibility in my post. You evidently didn’t read it.

And if there is nothing, there aren’t any propositions either. The necessary truth of a proposition is one thing, and its necessary existence another. A necessarily true proposition is such that if it exists, it must be true. But in case it doesn’t exist, it doesn’t have any truth-value, since nonexistent things don’t have any properties.

All potential things have potential properties. And all things that are logically possible are potential things. Nothing else is needed. This is addressed in my post. You evidently didn’t read it.

There are logically possible worlds which are truthless because they are proposition-/statement-/sentenceless. (Note that truthlessness is not the same as factlessness.)

This is gibberish.

Logically necessary truths are logically contingent entities.

Ditto.

…

The rest of your points are more of the same: illogical or unintelligible declarations, or points already addressed in my post and thus moot.

(And on abstract objects, read my discussion in Sense and Goodness without God before presuming to know my views in the matter. For those who are actually interested in that, it’s covered in chapter III.5.4, pp. 124-30.)

There cannot be any temporal relations between being and nonbeing = the absence of being. So it is logically incoherent to use words such as “precede”, “succeed”, “before”, “after”, “earlier than”, “later than”, “prior to”, “then” in this context. As soon as you say “In the beginning there was nothing, and then something came into existence”, your case is a logical nonstarter. The question as to when there was nothing is logically ill-posed.

“If we grant the metaphysical premise “there was once absolutely nothing,” then this epistemological argument becomes a metaphysical argument: it is then logically necessarily the case that there is an infinite multiverse.” – R. Carrier

The fatal problem is that this premise is “ungrantable”, because the little words “was” and “once” make it logically inconsistent and thus necessarily false. For it implies:

“There was a time when spacetime didn’t exist.”

This is logically impossible, because, necessarily, spacetime has always existed, i.e. there has never been a time when spacetime didn’t exist. Spacetime exists at all times. Note that this is true independently of whether or not its past is finite.

Not on my definition of nothing. Which I explain in the post. So you evidently didn’t read it carefully. (Indeed, I actually argue what you just did, that “necessarily, spacetime has always existed,” so for you to think this is a rebuttal really demonstrates you aren’t reading my article.)

“The question as to when there was nothing is logically ill-posed. – Myron

Well, if it’s not ill-posed, the only meaningful answer is: There was never nothing, and there couldn’t ever have been nothing. For the spatiotemporal world has always existed. (Note that “has always existed” isn’t synonymous with “has an infinite past” or “has no finite age/duration”.)

That’s certainly possible. And I even discuss that possibility in the article. The rest of the article only addresses the “what if there wasn’t” alternative. In other words, it does not assume the premise P1 is true, it argues what follows if the premise P1 is true. I explain this very carefully early on in the post. So again, you evidently aren’t reading it carefully.

“It is logically impossible for logical truths not to exist.” R. Carrier

A truth is a true proposition/statement/(declarative) sentence, and if it’s logically impossible for logical truths not to exist, then the existence of propositions/statements/(declarative) sentences is logically necessary.
Propositions and types of statements/sentences are abstract objects, and from the naturalistic point of view—and, as far as I know, you are a metaphysical naturalist—realism about abstracta (aka platonism) is generally hard to defend, or even indefensible. Anyway, I doubt that there is no possible world where there are no propositions/statements/sentences. Of course, in such a world where there are no truth-bearers, there are no truths either. But there is nothing contradictory about a truthless world. Of course, truthless worlds aren’t factless worlds, with facts being actual states of affairs.
But nothingness as the absence of a world is not one of the possible worlds.
The empty world is not the absent world.
One cannot even consistently describe there being nothing as a fact or state of affairs, since facts and states of affairs are entities.

Dear Mr. Carrier, I really don’t know why you deleted all my comments. They were neither off-topic nor otherwise improper. It took me some time and effort to write them, and now I see it was a waste of time and effort. Thanks for nothing!

Oops! I can suddenly see and read all my comments again. But there’s still “Your comment is awaiting moderation” added to them. Is there a technical problem with your blog? Do comments disappear for a while and then re-appear? To make a long story short, if you didn’t actually delete all my previous comments as I thought you did, I beg your pardon.

That’s a good question. I don’t know what different browsers show different users who have comments in moderation; it’s interesting to hear that some show you comments that you put in moderation that are still waiting (maybe this has something to do with cookies and logins, I don’t know). All I can confirm is that they sit in the moderation queue until I approve or reject them. Almost all get approved (indeed, by applying full moderation, it seems this has driven nearly everyone to follow my comments policy at long last). But as to what happens on your end in between, I have no idea!

At the risk of being slightly off-topic here, seeing as Richard linked his initial comment policy above, I thought I’d add this link to my new comment on the “Comments Crazy!” thread, which is where Richard explains the change to full moderation on the blog. My comment specifically addresses the “Your comment is awaiting moderation.” message for the benefit of commenters – in short, always make sure you’re logged in with your FTB account prior to posting here.

I’m not unsympathetic to the argument, but I don’t see how P3 doesn’t beg the question.

“P3: Of all the logically possible things that can happen when nothing exists to prevent them from happening, continuing to be nothing is one thing, one universe popping into existence is another thing, two universes popping into existence is yet another thing, and so on all the way to infinitely many universes popping into existence, and likewise for every cardinality of infinity, and every configuration of universes.”

You seem to be assuming that a universe popping into existence from nothing is logically possible. Isn’t this what you are trying to prove?

If that is logically impossible, then there would have to be some inalienable property of nothingness that prevents it. Certainly, if someone can demonstrate such a thing syllogistically (without simultaneously proving nothingness itself impossible), then we will have proven that something has always existed. Then the debate would turn to what that is.

But until that demonstration arises, there is no known property of nothingness that prevents anything from happening. That is indeed what P2 states, and early in the essay I give arguments for P2 being entailed by P1 (I didn’t just assume it was true). P3 is then entailed by P2. The rest follows. Thus, you would seem to want to challenge P2, not P3.

The basic thrust of your argument seems to be that anything that is not (logically) prohibited is compulsory (your argument is framed as a “lack of prevention” being responsible for everything).

I’d agree with this, but the issue is where “thingness” comes from; conventional dualist ontology requires there to be “things” that behave mathematically, but that the “thingness” itself is some sort of non-mathematical dasein; MUH says that the mathematics *is* the things (a monism). I don’t think your argument holds unless you agree that “thingness” is a mathematical (logical) property; in which case your argument is indeed equivalent to MUH. Without this premise (which I certainly believe is quite defensible), you will beg the question.

1. As for logically necessary beings, my contention is that nothing can be such that the denial of its existence implies a contradiction.

2. There can be no “state of nothing(ness)” because states are necessarily states of something, and a nothing/nothingness isn’t anything but nothing. That is, there is and can be no state unless there is something which is in that state. For example, it is illogical to say that there is a state of anger but nobody who is angry.

Merely possible things, i.e. things whose existence is possible but nonactual, are nonexistent things, and nonexistent things do not have any properties whatsoever. Do you really believe that if there were no actual things, there would still be merely possible things?

4. As for abstract objects:“‘Abstract objects’ are not really objects. They are sometimes called ‘universals’ because they are universally held in common by particular things. But they are also called ‘abstract’ because they are not particular things, but qualities or properties that are ‘abstracted’ from individual cases. …In the simplest terms, an abstraction or a ‘universal’ is a potential pattern of experience, a repeatable pattern of matter and energy in spacetime. …In order to talk and think about these occasions, we invent a word that refers to that common pattern, and that is an abstraction.”

1. Some abstract entities are properly called objects (e.g. propositions, numbers, sets, geometric figures, linguistic types), and some aren’t (e.g. universals). For universals are properties or relations rather than objects. Moreover, only Platonic, transcendent, instantiation-independent universals are properly called abstract, because Aristotelian, immanent, instantiation-dependent universals (as contemporarily championed by David Armstrong) are properly called concrete.

2. What you describe as “abstraction” is the psychological process of concept formation. But concepts as “abstract ideas” in the Lockean sense aren’t abstract in the nonpsychological, Fregean sense of the term. Abstract ideas in the psychological sense are mental representations and thus mental entities, whereas an abstract object or entity in the nonpsychological sense is neither mental nor physical.
According to the nonpsychological conception of abstracta, Locke’s abstract ideas are actually concrete rather than abstract, because they are mental entities.
Of course, an ontological naturalist can unproblematically affirm the existence of abstract or, better, abstracted concepts/ideas as mental entities. But a consistent ontological naturalist can hardly believe in abstracta which are neither mental nor physical, or, particularly, in instantiation- and spacetime-independent universals. (But the belief in intraspatiotemporal and instantiation-dependent, Aristotelian-Armstrongian universals is fully compatible with ontological naturalism.)

I wholly disagree with your metaphysics. But my views are already well known on that, I needn’t repeat them (besides the full section in my book, not just that one isolated quote, see for example my past blogs on ontology).

The bottom line is that if we grant your proposition that “there can be no state of nothingness” then you are in agreement with the half of my article that discusses what follows if indeed that is the case. The rest of my article only addresses what follows if that isn’t the case.

“A sentence is a structure in a language. Truths existed even when language didn’t. So obviously truths are not sentences. Sentences describe truths.” – R. Carrier

Where there are truths, there must be truth-bearers. If the truth-bearers aren’t (concrete) linguistic sentence-tokens or (abstract) sentence-types, then they are nonlinguistic and language-independent propositions (Fregean thoughts), which are abstract objects—”abstract” in the sense of “neither mental nor physical”. So, if the truth-bearers are propositions, then truths are simply true propositions. Some think propositions exist necessarily, in all possible worlds, but this view appears inacceptable and indefensible to me.

I do not know what the sentence “Where there are truths, there must be truth-bearers” means. You seem to have some idea that there must be thoughts or something for truths to exist. Either you are confusing two different concepts if truth (truth as belief-state and truth as fact) or you are stating something metaphysically dubious. Any fact is true that exists. All it therefore requires is that it exist. No other thoughts or concepts or ideas or belief states or anything need exist.

“I do not know what the sentence ‘Where there are truths, there must be truth-bearers” means.” – R. Carrier

It means: “Where there are truths, there must be things that are true.”

The most plausible candidates for the role as primary truth-bearers are language- and mind-dependent statements (abstract statement-types or concrete statement-tokens) and abstract, language- and mind-independent propositions, which are expressed by statements.

Thoughts (in the non-Fregean, psychological sense), beliefs, judgments, and assertions are secondary truth-bearers. Their truth (or falsity) depends on the truth (or falsity) of the respectively corresponding statements or propositions.

Both statements and propositions represent states of affairs, and if they are true, they represent actual, obtaining states of affairs, i.e. facts. I know that others use “true statement/proposition” synonymously with “fact”, but I consider it ontologically serviceable not to do so.
Accordingly, a truth is a true statement or proposition, and a fact is an actual state of affairs. Truths aren’t (identical with) facts; truths represent facts. The existence of truths depends on the existence of statements/propositions, but the existence of facts doesn’t depend on the existence of statements/propositions that represent them. What the existence of facts depends on is the existence of objects, properties, and relations.
The absence of truths doesn’t entail the absence of facts. A language- and mindless world is a truthless world but not a factless world.

Then you are using “truth” in a different sense than I do in the article. In which case your points are all irrelevant to what I say in that article. If you want to address what I say in the article, you have to consistently employ the same meanings of terms that I do.

“When absolutely nothing exists, a timeline can spontaneously replace it, because that is then among the things that can happen.” – R. Carrier

A being can be replaced with another being, but nonbeing cannot be replaced with being, since if there were nothing, there would be nothing—no it—to replace. So your statement is illogical.
The fundamental problem with trying to reason about nothingness, the absence of being/existence/actuality/reality is that

“Our conceptual machinery breaks down in trying to explicate the idea of pure nothing.”

When could the transition from there being nothing to there being something have taken place? Could it have taken place instantaneously at t = 0? No, because nothing can change or happen “during” a durationless instant. If it could, the states of affairs of there being nothing and there being something would obtain at the same time t = 0, which is logically impossible. Could the transition have taken place at some time t* earlier or later than t = 0? No, because there is no time t* earlier than t = 0, and for all times t* later than t = 0 it is no longer the case that nothing exists; that is, the absence of being is absent at all times later than t = 0. So, it turns out that the transition from the absence of being to the presence of (temporal) being couldn’t have occurred at all, because it couldn’t have occurred at t = 0, nor at any time earlier or later than t = 0.

The more I reflect upon it, the more illogical it appears to me to speak of a transition from there being nothing to there being something. Transitions from one state of affairs to another are change-involving events, but the absence of existence cannot even consistently be called a state of affairs. Even if one grants the existence of negative state of affairs such as Barack Obama’s not being a woman, there is still the existent Barack Obama. But if nothing at all exists—no objects, properties, or relations—, then there are neither positive nor negative states of affairs. One might be tempted to call its not being the case that something exists the absolute negative state of affairs; but then one ends up with a self-contradiction (“The absolute negative fact that nothing exists exists”) or with an unintelligible use of the ontological category “state of affairs”/”fact”.

We can consistently say that spacetime has a temporal boundary in the past, but we cannot meaningfully and coherently say that at that boundary (t = 0) there occurred a change or event describable as spacetime’s “beginning to exist”, its “coming into existence”, or its “popping into existence”. Nor can we meaningfully and coherently speak of a transition from there being nothing to there being something, because such a transition would presuppose the existence of a temporal relation between the former and the latter, which is logically impossible. It is plainly illogical to say that “There was nothing, and then something began to exist/came or popped into existence.”
(FYI: I do know the difference between the temporal “then” and the logical “then”.)

For example, you write above:“Of all the logically possible things that can happen when nothing exists to prevent them from happening, continuing to be nothing is one thing…”

If nothing existed, then nothing would or could continue to exist, since nothing can continue to exist unless it exists and exists in time. But there being nothing isn’t a temporal “state of affairs”.

Whether time would come to exist or not is one of the things that can happen. In the absence of time, everything happens simultaneously (at the speed of light, for example, where time equals zero but all past and future events exist at once). It is therefore incorrect to conclude nothing can happen. That requires assuming a hypertime is needed, which it isn’t. It isn’t in relativity theory. It isn’t in logical fact. It isn’t in geometric reality.

For a reference frame moving at the speed of light, nothing happens. Nothing happening outside it in the rest of the universe can be detected, nor is there any time to allow anything to happen within itself.

And yet, outside that reference frame of the object, events continue to happen. It would seem to us that all these events must happen simultaneously from the point of view of that reference frame, but that is to forget that that reference frame doesn’t really have a point of view because it has no time in which to observe anything. It is absolutely frozen. Nothing can happen from its point of view. Nothing can happen within it.

It’s for these kinds of contradictory reasons that moving at the speed of light is impossible for ordinary matter.

But we’re considering all of reality having no time, not just one reference frame. For the analogy to apply, there would have to be other reference frames within which events could happen apparently simultaneously.

For example, if we are considering one hypothetical universe having no time, we are free to imagine events in other universes happening “simultaneously”.

However, other reference frames cannot exist outside reality, and there is no time within reality, therefore nothing can happen.

First, you can have a universe with space and galaxies in it but no time. It’s logically, and geometrically, possible. In reality, it would have one instant of time, that moment in which all those galaxies simultaneously exist. It would be a frozen universe, as you say. But it’s still possible. Thus all we need calculate is the probability that such a universe (or indeed several) exists. Note that such a universe will not have existed from past eternity, because it contains no eternity. It contains only one instant of time. And its contents will have a definable probability on quantum mechanics, a probability of such a universe instantly coming to be. No additional time is needed for that. It just either exists or it doesn’t. The amount of time that decision takes is zero.

But other universes are far more probable on quantum mechanics. Ours, where (if we suppose the Big Bang originated time, which we actually have no evidence of anymore, but it’s a possibility) an instantaneous appearance of a vacuum state kicked off an extended time dimension. But from a perspective outside of time, there is no difference between this universe and the hypothetical one just proposed above. Outside of time you have simply the instantaneous appearance of the whole universe, all past and future at once, as a single 4D world-tube. It just instantly exists. Or doesn’t. It’s all just a matter of probability. In relativity theory, the entire universe, and all its future, exists at the same moment of time relative to a hypothetical ray of light approaching it from outside.

Thus it is not that you need a time in which nothing can become something, because that can happen in zero time, just as that hypothetical ray of light will see our universe have done. Just as you can have the instantaneous appearance of extended space in a zero-time frozen universe where nothing changes from one moment to the next (a photograph is itself a model of such a thing), you can have the instantaneous appearance of extended time. The timeline, like the spaceline, appears instantly, in zero external time. Or, again, doesn’t. Depending on how the cosmic existential dice roll.

Thus it is not that you need a time in which nothing can become something, because that can happen in zero time, just as that hypothetical ray of light will see our universe have done. Just as you can have the instantaneous appearance of extended space in a zero-time frozen universe where nothing changes from one moment to the next (a photograph is itself a model of such a thing), you can have the instantaneous appearance of extended time. The timeline, like the spaceline, appears instantly, in zero external time.

This is where I both agree and disagree with you emphatically. I get that it takes zero time for a universe to exist. And that’s the problem. Because your initial premise is that nothing exists. If it takes zero time for the decision to be made, then in the beginning, there is not “nothing” but an infinite number of universes. Your conclusion contradicts your premise.

The only way to resolve this contradiction would be to propose some kind of hypertime within which the state of reality can evolve from nothing into everything. I don’t believe in hypertime – I think all universes have always existed as 4D structures. I reject “In the beginning there was absolutely nothing” because if that was the case then nothing is all that could ever exist.

I accept your view that a universe would have to have at least a single instant of time. To explain my earlier arguments, I had been describing this as there being an absence of time. You can mentally find and replace most of the uses of “time” in these arguments with “timeline”.

The difference between a single instant of time within a timeline, and the temporal singularity I believe would be consistent with absolute nothingness is the subject of this blog post.

I’ll summarise the argument for you here as I doubt you have time to read the blog post at the moment.

The hypothetical singularity at the origin of a universe is only a singularity with respect to the three dimensions of space. All of these dimensions is contained within a single 3D point, however it does not contain all of the time dimension. From that point extends a timeline, therefore the point cannot be said to be a temporal singularity.

I believe that spacetime in a state of absolute nothingness would have to be zero-dimensional. If you disagree, then how many dimensions do you believe space would have, for example? Three seems arbitrary – there’s no obvious reason why existence should require three spatial dimensions. I doubt you even assume the need for even one dimension, and are happy to say that there are zero dimensions spatial dimensions in a state of absolute nothingness (i.e., all of space is a single point).

If there are no spatial dimensions, then I don’t see why there should be any time dimension. All of time is reduced to that same point of spacetime. So when I say there is no time, I mean there is no time dimension. There is only a single point of spacetime, which you call your single instant of time.

It is in the absence of this time dimension that I maintain nothing can happen. All points of time are the same point, therefore the description of reality cannot change.

So when I say “time” cannot come into existence, I mean a “time dimension” cannot come into existence. And the same argument holds. If a time dimension were to come into existence instantaneously, as you state it would have to, then you would be maintaining that “In the beginning there was absolutely nothing (including, in my view, no time dimension)” at the same time as you maintain “In the beginning, there was a time dimension”.

I see these two positions to be in contradiction and cannot reconcile the two. I explain why in detail on the blog post above as well as in this one where I discuss the concept of hypertime as raised by you.

In one of those I give the example of a picture of a pool ball on a snooker table. You can’t tell by looking at the picture whether the ball is moving or not, because in the absence of time the property of momentum is hidden. Considering a single point of spacetime at the beginning of a timeline and comparing it to a temporal singularity is the same thing. They look identical in the absence of time, but when you “unfreeze” your viewpoint then the timeline origin point has a hidden property (the time dimension) that the temporal singularity does not.

There’s also the analogy to the Zeno arrow paradox. I think that arguing that a time dimension can spring into existence from a single instant of time is almost like a corollary to this paradox, which maintains (basically) that movement is impossible because at any given point in time the arrow is stationary. Both arguments are wrong because they assume that it is valid to draw conclusions about what can happen over time by considering only a single instant of time.

Continuing the analogy with motion, my argument that a time dimension has to exist from the beginning is analogous to Newton’s first law.

Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.

In this view, the temporal singularity is a body at rest. It will never move because there is no force to move it. There is no time within which the state can change and allow this point to become a line.

The time we experience is like a body in motion. It is in motion not because something kicked it off, but because it has been in motion since the beginning of its existence, or eternally if time didn’t have a beginning. It was never at rest.

And because I think P1 implies that time was at rest, I don’t think your argument follows.

I understand that P1 says there are no laws, so perhaps that is a weakness of the analogy. But I remind you that my objection is not based on the assumption of a law but on the logical impossibility of two mutually contradictory descriptions of reality (“absolute nothing” vs “infinite universes”) being true at the same instant of time (“the beginning”).

If it takes zero time for the decision to be made, then in the beginning, there is not “nothing” but an infinite number of universes.

Yes. If that’s what existentially falls out (there is, after all, an infinitesimal but nonzero probability that it won’t, in which case there will have been nothing and no universes, ever; which, obviously, isn’t how the existential dice rolled).

Unless by “in the beginning” you mean at the first point of spacetime. Then there certainly can be nothing there (except the spacetime point), and extending from that point an infinite number of universes containing stuff. Geometrically there is no difficulty with this.

But I assume you either mean by “nothing” the absence of any other spacetime points completely, or you are confusing this with the above. Either way, when I say “in the beginning there was nothing” all I mean is at the first point of spacetime. I do not make any assumptions about what then happens to extend from that. To the contrary, what will then extend from that is a product of random chance (there being “nothing” to decide what will extend from it). My argument then follows.

I believe that spacetime in a state of absolute nothingness would have to be zero-dimensional. If you disagree, then how many dimensions do you believe space would have, for example?

No, it would be one-dimensional, insofar as there is a difference between no location in time and a single location in time: what will exist at the start of all universes (or will exist alone, if no universes ever existed) is all space and time dimensions collapsed to one point (and insofar as that is not the same thing as being nowhere and never, that’s one dimension, not zero). What would extend from that point will then be random, per my argument.

And because I think P1 implies that time was at rest, I don’t think your argument follows.

The very phrase “time was at rest” assumes an A theory of time, which contradicts Relativity theory and is therefore probably incorrect. B theory corresponds to Relativity. Time does not “move.” It’s a static dimension like space. We see it as though it moves, but that’s an illusion created by our perspective. My blog on the ontology of time explains further, but I discuss the causes of the illusion in detail in Sense and Goodness without God III.3.6, pp. 88-96.

The question is, if we walk back to the first point of time and look around, what will we see extending from that point, given that there is no God? One timeline? Many timelines? No timelines? (the latter being what we’d expect on the theist’s ex nihilo argument, hence the fact that a timeline exists, on that argument, refutes atheism because the condition is supposed to be impossible; a God must be found there; my argument is a rebuttal to that argument)

There is no extra hyper-time in which a “decision” is made, as though some cosmic entity is twiddling its thumbs, staring at a nothing and deciding what to do with it. No. There instantaneously either is always nothing (aka there is never anything) or always something (like a multiverse). Which of those it is, is randomly decided. Because in the absence of anything prior (in the absence of “some cosmic entity is twiddling its thumbs, staring at a nothing and deciding what to do with it”), there is nothing to decide what will exist. Thus all possibilities are equally likely. My argument follows.

This decision does not occur “in” time. It occurs instantaneously at the first point of time. There is no “time” in which the “nothing” sits around waiting for something to happen (except, of course, that one single instant of time at which the nothing exists, but that is not an extended dimension but just a single instant, hence what extends from it is “instant”-aneous).

Just wanted to quickly address this point while you appear to be active online (I’ll respond to the rest when I have a chance):

No, it would be one-dimensional, insofar as there is a difference between no location in time and a single location in time: what will exist at the start of all universes (or will exist alone, if no universes ever existed) is all space and time dimensions collapsed to one point (and insofar as that is not the same thing as being nowhere and never, that’s one dimension, not zero).

I agree that in formal mathematical language a point is zero dimensional. But the question is whether “there is a difference between no location in time and a single location in time.” The answer is yes. So if you want to call a single location in time “zero dimensional” that’s fine, just don’t conflate that with “no location in time” (i.e. the absence of a time dimension). Mathematically, a lot can be contained in a zero dimensional point. And a zero dimensional point is not the same thing as the absence of any point.

My post is a bit long so I will make the most important points in bold to facilitate speed reading.Digressions are marked in italics

I agree that in formal mathematical language a point is zero dimensional. But the question is whether “there is a difference between no location in time and a single location in time.” The answer is yes. So if you want to call a single location in time “zero dimensional” that’s fine, just don’t conflate that with “no location in time” (i.e. the absence of a time dimension). Mathematically, a lot can be contained in a zero dimensional point. And a zero dimensional point is not the same thing as the absence of any point.

I’m not so sure that a zero-dimensional point is as interesting as you make out. The page you linked to is discussing a concept in topology which doesn’t appear to me to be the same thing.

In any case, the formal mathematical sense is that in which I am arguing that a point is zero-dimensional. I know of no sense in which you could argue that it is one-dimensional. I am not conflating zero dimensions with there being no point in time, so you appear to be attacking a straw man.

Instead, I am suggesting that to say there is “time” is to suggest there is a dimension of time. If there are zero dimensions, then there are no dimensions of time, and in my view there isn’t really any time to speak of at all. Yes, you could argue there is a single “instant”, “location” or “point”, but that isn’t enough to allow events to transpire (including the event of the creation of a time dimension).

This is not true time in my view. If you think it is, then assume I mean “timeline” or “time dimension” when I say time.

Yes. If that’s what existentially falls out (there is, after all, an infinitesimal but nonzero probability that it won’t, in which case there will have been nothing and no universes, ever; which, obviously, isn’t how the existential dice rolled).

I understand this part of the argument. If I characterise you as claiming there must be effectively infinite universes, you can take it that I understand that there will be an infinitesimal chance of no universes. If you think it is an incorrect characterisation I will try to word it differently.

Unless by “in the beginning” you mean at the first point of spacetime. Then there certainly can be nothing there (except the spacetime point)…

By “in the beginning” I am alluding to your P1. I don’t know exactly what definition you have for “beginning” here but I assume it corresponds to the initial state of reality.

The problem is that according to this definition, you draw a conclusion that contradicts the premise. “In the beginning there was absolutely nothing” becomes “In the beginning there are (very probably) an effectively infinite number of universes)”.

This transition happens in the absence of time and so must be instantaneous. And so both descriptions of reality must apply at the same instant. Those descriptions appear to me to be in contradiction, so you appear to me to be mistaken.

So I do not mean the first point of spacetime within a universe. However, I maintain that the point of spacetime at the origin of the universe is not, in fact, nothing. It is a point in 4D space-time. True time exists there. Time has “momentum” per my analogy, by which I mean there is a time dimension.

..and extending from that point an infinite number of universes containing stuff. Geometrically there is no difficulty with this.

Actually there is. Geometrically, nothing can extend from a point in a direction which is orthogonal to the available dimensions. On a 2D drawing, I cannot draw a line directly perpendicular to the page. As the point of space-time in a state of nothingness must be 0-dimensional, nothing can be extended from it (every direction is orthogonal to the available dimensions).

what will exist at the start of all universes (or will exist alone, if no universes ever existed) is all space and time dimensions collapsed to one point

No, what will exist at the start of all universes (important qualifier: which begin with a big bang-type singularity) is all spatial dimensions collapsed to one point. Time is not collapsed. If it were, there would be no timeline, nothing would happen and the universe could not expand.

However, it occurs to as I write this that a weakness of my argument is that gravity affects time. At a point of infinite density, I presume time would in fact stop completely. This is consistent with quantum mechanics driving modern physics away from the concept of a singularity at the big bang (as I believe Hawking joked, he became famous for showing that the universe began with a singularity and then became famous for proving it didn’t).

If you think this is a problem for my argument (and it may well be), then I may need to get clarification from a physicist on how it was ever plausible that the universe began with a singularity. If you think this is a separate issue, then please explain to me how all of time was contained in the singularity when here we are experiencing time outside a singularity.

The very phrase “time was at rest” assumes an A theory of time, which contradicts Relativity theory and is therefore probably incorrect.

No it doesn’t. The wikipedia article you linked to describes the “A theory of time” as maintaining that the future is undecided and so is objectively qualitatively different from the past, as opposed to B, which holds that they are essentially the same and can be viewed as a static path in four dimensions. This is not contradicted by what I said, especially given the context of the analogy I was describing (momentum => existence of time dimension).

In fact, any theory which maintains that the future is to be determined according to a probability distribution (such as non-deterministic interpretations of Quantum Mechanics and Ex Nihilo Merdae Fit for that matter!) would seem to be more consistent with A than with B.

The B theory of time would hold that time does not move, but then it would also hold that bodies don’t move, they just describe static world tubes in 4D space. My analogy still holds. When I said that “time was at rest” I meant (as should be clear from the analogy) that there was no time dimension. The rest of the argument follows: if there was no time dimension, then nothing can happen, including the creation of a time dimension.

I will read your blog on the ontology of time, however I don’t think our disagreement stems from any misunderstanding of the nature of time on my part. Whenever you explain time to me, I find in general that your explanations conform to the views I already hold.

The question is, if we walk back to the first point of time and look around, what will we see extending from that point, given that there is no God? One timeline? Many timelines? No timelines? (the latter being what we’d expect on the theist’s ex nihilo argument, hence the fact that a timeline exists, on that argument, refutes atheism because the condition is supposed to be impossible; a God must be found there; my argument is a rebuttal to that argument)

What we will see has to be one or many timelines, simply because we can “see” that there is at least one timeline. The theist’s question is “Why should this be the case?” Your argument is an attempt to answer this question, however I believe it is not a correct answer because it does not successfully demonstrate that timelines could arise spontaneously from absolute nothing.

I believe rather that it is impossible that there could be absolutely nothing (or more accurately, that a state of absolute nothingness is just one universe out of an infinite number of alternatives which all exist independently). Reality is necessary, as argued by Max Tegmark in the MUH. This is a better response to the theist’s question, in my view. It has the drawback of being highly unintuitive and difficult to grasp, however it has the virtue of being correct (as I would be happy to argue).

There is no extra hyper-time in which a “decision” is made, as though some cosmic entity is twiddling its thumbs, staring at a nothing and deciding what to do with it.

I agree and I have repeatedly stressed that I agree.

There instantaneously either is always nothing (aka there is never anything) or always something (like a multiverse).

The former agrees with P1. The latter contradicts it.

there is nothing to decide what will exist.

P1 decides that nothing exists. This cannot change without a time dimension.

This decision does not occur “in” time. It occurs instantaneously at the first point of time.

Agreed. The universe has always existed as a 4D construct. This is why P1 must be wrong: it is not true that “In the beginning there was nothing”, instead it is true that “In the beginning, there was everything”, or more properly, “Every universe which can be modelled mathematically exists eternally.”. There is no “beginning”, precisely because the “decision” (although I do not believe any decision is being made) occurs “outside of” time. It does not happen at the first point of time, it happens completely independently of time.

I don’t know exactly what definition you have for “beginning” here but I assume it corresponds to the initial state of reality.

It corresponds to t=1 (the first instant of time). Nothing more.

Do you see the difference?

You are imagining t=1 and there is no other t and “then” (in hyper-time) a t=2 pops into existence next to t=1, as if there was some other “time” in which there was only one instant of time and then after some of that “other” time passed, more instants of time appeared. But that’s incorrect. There is no hyper-time, nor any need of it. If in the beginning, i.e. at t=1, there is nothing, then are there any other points of time, or will there only ever be just that one instant of time? Once you answer that question (after accepting that there is nothing at t=1 to decide whether there will be a t=2 or not, etc.), you end up with what exists: either t=1 alone, or t=1 with many more t points attached. Obviously, the latter is what happened. All we need figure out is how likely that was (vs. how likely it is that there would have only ever been a t=1).

On a 2D drawing, I cannot draw a line directly perpendicular to the page. As the point of space-time in a state of nothingness must be 0-dimensional, nothing can be extended from it (every direction is orthogonal to the available dimensions).

You are confusing things in space with space itself. I am talking about whether there will be only a “page” or a cube or a hypercube or an infinicube etc. in the first place. There being nothing to decide that, what it will be is random. Odds are, then, there will be infinitely many dimensions. Our universe is just one pocket in that matrix (in which all but a few of those dimensions are collapsed, either totally or into Calabi-Yau spaces).

I believe it is not a correct answer because it does not successfully demonstrate that timelines could arise spontaneously from absolute nothing.

You are asking for a hypertime here. That’s not valid.

Again, think of what shapes can exist, geometrically, taking time as just one dimension of a shape. On that, “timelines could arise spontaneously from absolute nothing” is obviously true. I can draw a shape where at one corner there is nothing and extending from it are dozens of dimensions (whether of time or not, doesn’t matter). So obviously it is not impossible to have a nothing-point from which extends many timelines.

So again, you are stuck on hypertime. You are imagining that the nothing point floats around in some extra “timeline” and “then” out of it pops other timelines. That’s incorrect. The only question is whether, there being any nothing point at all, there will be timelines extending from it or not, and how likely that is. No extra “time” is needed to decide this. There is no “hypertime” in which the nothing point floats around, clock ticking, waiting to decide whether more timelines will pop out of it. If any will pop out of it, they will do so instantly, the very single moment the nothing point exists. There will never be a “hyper time” in which there was nothing and no other timelines (except at an odds of infinity to one against, as I calculate–in other words, that what would exist would be just nothing, with no timelines, has odds of infinity to one exist).

“All necessary truths necessarily exist, therefore, the truths of probability theory exist when nothing exists (otherwise we would have a logically impossible state: a state in which logically necessary truths were not true).” – R. Carrier

Again, the existence of truths entails the existence of truth-bearers, i.e. of things that are true (or false). The things that are true (or false) are statements or propositions. Truths are true statements/propositions. If a statement/proposition is contingently or necessarily true, then it exists; but this doesn’t imply that if a statement/proposition is necessarily true, it necessarily exists. I’m sorry, but you’ve committed a fallacy here!
For []Tp –> E!p doesn’t imply []Tp –> []E!p.

Your assumptions that necessary truths, i.e. necessarily true statements/propositions (such as logical laws), exist in all possible worlds, and that there is a possible world in which nothing exists but necessary truths are extremely platonistic and thus antinaturalistic, because they entail the ontological postulation of statements/propositions as language-, mind-, and spacetime-independent abstract objects and even as necessary existents. I utterly fail to see how these assumptions and their ontological implications could be successfully and coherently integrated into the naturalistic worldview. Of course, you don’t have that compatibility problem unless you are a (metaphysical) naturalist. But, as far as I know, you are one, aren’t you?

That’s all incorrect. For a fact to be true is simply for it to exist. Propositions about that fact do not have to exist for the fact itself to exist.

And when the fact in question is a potential, all that has to exist is the potential, not the actual thing that can potentially happen or exist. At most you can argue that for any potential to exist, there must be a place and time for it to exist, which, if correct, entails the necessity of spacetime. For then it would be self-contradictory to say spacetime doesn’t exist. Because if it didn’t, contradictory states of affairs would be possible. Which is by definition impossible.

And so on. All of which is already dealt with in my original post and in comments above.

Can’t I meaningfully say that it was the absence of guns that prevented people living in 1,000 BCE from shooting themselves? Can’t I meaningfully say that it is the absence of food that prevents many people in Africa from surviving? Can’t I meaningfully say that a lack of money prevents people from buying something? Can’t I meaningfully say that the absence of time would prevent things from happening?

Those are all statements based on the assumption of the existence of laws and forces governing what will happen. When nothing exists, neither do such laws and forces. So then, no, it would be self-contradictory to say that the absence of something “prevents” another thing from happening. Because that presupposes laws exist that govern what happens, e.g. conservation of energy.

1. If facts are defined as actual, obtaining states of affairs, then speaking of true/false facts is a category mistake, because states of affairs are not the kind of things that can be true/false.
Moreover, one can consistently speak of nonexistent states of affairs but not of nonexistent facts, because actual/obtaining states of affairs are existent states of affairs, so that a nonexistent fact would be a nonexistent existent state of affairs.
2. If facts are defined as true propositions, then speaking of false facts is a contradiction in terms, because then “false fact” means “false true proposition”.
Given this conception, “The fact that p exists” means “The true proposition that p exists”, which is equivalent to “The proposition that p is true”.
However, “The necessarily true proposition that p exists”/”The proposition that p is necessarily true” doesn’t imply “The proposition that p exists necessarily”/”The proposition that p must exist” but merely “The proposition that p cannot exist without being true”.

“Propositions about that fact do not have to exist for the fact itself to exist.” – Carrier

Above you seem to treat facts as true propositions, and here you seem to differentiate ontologically between facts and propositions. But you have to make a clear decision, since facts are either true propositions or actual states of affairs. Facts as actual states of affairs, or at least most of them (the natural ones), do not depend for their existence on the existence of corresponding propositions that represent them. Therefore, the famous Tarski principle

p iff “p” is true

is false, because it entails that for every fact there is a corresponding true proposition representing it. But the principle can be saved in a qualified form as follows:

(p & “p” exists) iff “p” is true
–“And when the fact in question is a potential, all that has to exist is the potential, not the actual thing that can potentially happen or exist. At most you can argue that for any potential to exist, there must be a place and time for it to exist, which, if correct, entails the necessity of spacetime. For then it would be self-contradictory to say spacetime doesn’t exist. Because if it didn’t, contradictory states of affairs would be possible. Which is by definition impossible.” – Carrier

Potentials aren’t facts; they are dispositions, i.e. dispositional properties aka powers. And where there is a power, there must be something, some (actual) thing (object/substance) which possesses or instantiates it. There are no unpossessed or uninstantiated powers, but there are unmanifested powers; and the existence of powers doesn’t depend on the existence or occurrence of their respective manifestations.
Powers exist where their possessors exist, because they are part of them.
If by “potentials” you shouldn’t mean dispositional properties but purely possible things/events, i.e. possible but nonactual things/events, then I deny that there exist any such pure or mere possibilia.

That’s grammatically false. Not replacing is the absence of change. Replacing is the presence of change. Thus “replacing an empty box with a full one is not to replace anything” is just semantic legerdemain, not a logical argument for the impossibility of it.

My definition of nothing is clearly explained and defended in the original post.

Agreed.

Has there been a misunderstanding? I’m not asking you to define “nothing” again – your definition of nothing in P1 is quite clear. I’m just asking you to clarify the apparent contradiction between your premise “In the beginning there was absolutely nothing”, with your statement above “Thus, there was never a time when there was nothing.”

I think this question is quite clear and I’m sure you have a good answer – you were speaking in two different contexts perhaps, or you have two different ideas of nothing. I’m just asking what that explanation is for the sake of clarity. Please address this.

You were talking about time. My definition of nothing includes time. Thus, if we call time something, as you were, then there will never have been a time when there was nothing. But since (as I argue when constructing my definition of nothing) the absence of at least one point of time is logically impossible, the most “nothing” that can logically exist is a nothing that includes one point of time, and then something more exists only if time is extended beyond one point. Which can occur, or not, instantaneously, i.e. it either exists or not, and then all we need do is calculate the probability of each possibility, when nothing exists to decide what will exist.

On the alternative notion that there can be a state of nothing in which there is not even one point of time, you get a logical contradiction: a state of affairs that “never” exists. That which never exists never exists. Therefore no such state of nothing can ever have existed. We therefore can rule it out from the get go. If theists argue that in the absence of god a nothing would have existed that never exists, then they are contradicting themselves and they have no argument. They can only have an argument if they adopt my definition of nothing. But when they do that, the rest of my argument follows. QED.

You’ve resolved the contradiction/confusion perfectly. It wasn’t clear to me that you were using my sense of “nothing” in the latter sentence, nor that you do categorically state that it is impossible for time not to exist.

It seems, therefore, that I was correct to interpret your argument as assuming that time exists. However, you maintain that this assumption is based on the necessity of time’s existence rather than being an arbitrary premise.

I disagree with this but it has refocused the argument very helpfully.

“In the absence of time, everything happens simultaneously…” – Carrier

Simultaneity is a temporal relation, and thus it cannot be instantiated in a timeless world. The inhabitants of a timeless world cannot coherently be said to exist or occur simultaneously with one another, since for x and y to be simultaneous with one another is for them to exist or occur at the same time.

That’s correct. And all events in our universe exist and occur at the same time–in at least one reference frame. There is therefore nothing illogical or impossible about that. See my blog on the Ontology of Time. Thus all we need is one instant of time. Which, as I’ve argued, necessarily exists.

“Not replacing is the absence of change. Replacing is the presence of change. Thus ‘replacing an empty box with a full one is not to replace anything’ is just semantic legerdemain, not a logical argument for the impossibility of it.” Carrier

An empty box is something rather than nothing, and so it is certainly not the case that to replace something empty with something full is not to replace anything. What I said is that to replace nothing with something is not to replace anything (but to place something somewhere).

That is immaterial to the point. If you have nothing at t=1 and then something at t=2, you have replaced nothing with something. The only issue you are stuck on is that for nothing to exist at t=1, at least one thing must exist at t=1, namely time. Thus it then depends on what sort of nothing you are talking about. A nothing that lacks even an instant of time is logically impossible and thus moot (no argument can ever proceed from a premise that such a nothing existed, exactly as my article explains). That leaves my nothing, which contains time, which is the most “nothing” you can ever logically possibly have. Thus you are just quibbling over the definition of nothing. Which is a waste of time. As I’ve explained, the “nothing” you want there to be, cannot ever have been. So it is moot to my article’s entire argument.

While I disagree with the original post in general, I have to say I’m with Dr. Carrier on this issue. Replacing nothing with something seems valid to me. It’s all just a question of semantics anyway and is unlikely to shed any light on the question at hand.

(BTW, the mathematician in me rebels at “t=1″ so I’ll refer to “t=0″ if you don’t mind.)

If you mean t=0 is the first instant on our timeline, then this does not correspond to absolutely nothing, because there was definitely not absolutely nothing at the first moment of this universe’s timeline. There was a timeline (time dimension) for a start.

Obviously, the latter is what happened.

This isn’t obvious at all. It may be the case that P1 is false, and so the explanation for our current existence may be otherwise. So you can’t use the fact that we exist to argue that something can arise out of nothing.

You are confusing things in space with space itself.

That’s funny, as I would level precisely the same accusation at you.

If we’re discussing absolute nothingness, then all of space-time was a 0-D point. “Space itself” was a 0-D point. That’s why I’m discussing “space itself”. You’re the one making comparisons to the big bang singularity, which is simply one point within 4-D space-time, just as the apex of a cone is a point on a 3-D structure. It’s not the same thing at all. It could only be the same thing if it was also a temporal singularity and so contained all of space-time, which it clearly does not.

I am talking about whether there will be only a “page” or a cube or a hypercube or an infinicube etc.

And P1 answers this. “There was absolutely nothing” implies there was neither a page nor a cube nor a hypercube nor an infinicube, but a single zero-dimensionless point. There’s no point speculating what else there might be because you’re contradicting your premise.

For what it’s worth, I agree with almost all of what you say except that you need to forget P1. Your argument does not depend on P1, even though that appears to be a ludicrous statement on the face of it. If you scrap P1 and basically assume that the universe exists because there’s no reason it shouldn’t (which, in a nutshell, is the gist of what you’re saying), you’re left with the beginnings of the MUH (Mathematical Universe Hypothesis).

I can draw a shape where at one corner there is nothing and extending from it are dozens of dimensions

You can only do that if you have space to draw the dimensions. You can’t draw lines on a piece of dust. You can’t draw planes on a hair. You can’t draw cubes on a page. You can’t construct hypercubes out of toothpicks.

If space-time is zero-dimensional, you can extend nothing at all.

What I’m contending and what you don’t seem to appreciate is that in absolute nothingness, there need be no space at all, no time at all. It’s not that space is empty or all matter is condensed into a point within space, it’s that there is no space, or equivalently space-time is a 0-D point.

You are asking for a hypertime here. That’s not valid.

No, I’m really not. I’m just pointing out that you can’t give a consistent account of how the state could have changed from absolute nothingness in the absence of any kind of time. Asserting that no hypertime is needed because it happens instantaneously is just contradicting P1 – if it happens instantaneously then there is a time dimension in the beginning, which is contrary to “absolutely nothing”.

Let me break down my argument into numbered points. Please give me your evaluation of each one, because I feel like we’re talking in circles here. I feel there are some subtleties of my argument that you’re skimming over, perhaps because you’re busy.

1. “Absolutely nothing” implies that space-time or reality has no dimensions.
2. If any space or time can be said to exist at all, it exists as what amounts to a single dimensionless point in 0-D space.
3. Postulating the creation of new space-time dimensions or universes entails a change of state.
4. Changes of state can only occur within the context of a timeline.
5. Timelines can only exist if there is a time dimension, so if statement 1 is true there is no timeline. Furthermore, no new timelines can arise because of statements 3 and 4.
6. We need not suppose that there was ever a state of “absolutely nothing”, and thus statement 5 is not contradicted by our observation of a timeline.
7. A geometrical point within 3-D or 4-D space is not the same thing as there being effectively being no space (space-time is 0-D).
8. I do not believe that hypertime explains how our universe arose. Instead I argue that P1 is false.
9. The concept of hypertime may be ridiculous, but it only arises as a consequence of logically considering the implications of your premises. I am not arguing for hypertime – I am arguing that you are implicitly assuming it even if you don’t realise it.
10. If no hypertime is needed because the decision is made “instantaneously”, then at the same instant we find “absolutely nothing” and infinite dimensions, timelines, universes. This is a contradiction.

(BTW, the mathematician in me rebels at “t=1″ so I’ll refer to “t=0″ if you don’t mind.)

I’m not sure if I should. Arbitrary semantics are fine, until you start to reify them. Insofar as “t=0″ means there is no time, then it’s inapplicable to my argument (as I argue there necessarily was one instant of space-time). If we ordinally count instants of time, then the first instant is t=1. You can label that t=0 if you want to. As long as you don’t drag your metaphysics along with it.

If you mean t=0 is the first instant on our timeline, then this does not correspond to absolutely nothing, because there was definitely not absolutely nothing at the first moment of this universe’s timeline. There was a timeline (time dimension) for a start.

Now you’re talking in a circle. We’ve been over this. I argue in my blog post that it is logically impossible for there to be absolutely no time. The most “nothing” there can ever have been, must have been, therefore it must have a location in time. Otherwise, you are saying there was never nothing, which denies P1, and the theist’s argument for God fails (which option my argument allows; you also forgot that–so on that, see next).

You are therefore defining “absolutely nothing” as something that is logically impossible (it can’t ever have existed…literally: existing at no time, it will never have existed). Which possibility I address right near the top of my blog post. My argument only pertains to nothings that could have existed, i.e. nothing-states that are logically possible. No other nothing-states matter.

It may be the case that P1 is false, and so the explanation for our current existence may be otherwise. So you can’t use the fact that we exist to argue that something can arise out of nothing.

More talking in a circle. I already acknowledge the possibility that P1 is false in my blog post. Indeed, that possibility is a major component of my overall argument and I discuss the option several times. You seem to have completely lost track of that fact.

And P1 answers this. “There was absolutely nothing” implies there was neither a page nor a cube nor a hypercube nor an infinicube, but a single zero-dimensionless point. There’s no point speculating what else there might be because you’re contradicting your premise.

You still aren’t getting it. “There was absolutely nothing” implies there was neither a page nor a cube nor a hypercube nor an infinicube, but a single zero-dimensionless point at (ordinally) t=1. But that is a tautology. That says nothing about what is attached to that single zero-dimensionless point.

For example, if I form a triangle out of seashells and leave the corner shell off at coordinate x,y = {0,0}, I can say there is nothing at x,y = {0,0}. That in no way entails there are no other shells, much less no triangle.

There is simply no contradiction here.

Only when you introduce hyper-time can you create a contradiction. In ordinal hyper-time t=1 there are no shells, neither at x,y = {0,0} nor anywhere else, then at ordinal hyper-time t=2 there are still no shells at x,y = {0,0} but now also shells forming a triangle beside it. I am not using hyper-time. When I say there is nothing at x,y = {0,0} all I am saying is that there is nothing at x,y = {0,0}. I am not saying if anything else will exist beside it. That has to be determined. And that is what the rest of the argument determines: what most likely will exist beside it. That “nothing” will exist beside it I then find to be infinitely improbable. Therefore the theist’s argument that if x,y = {0,0}, then there will only ever be x,y = {0,0}, is false.

Thus:

1. “Absolutely nothing” implies that space-time or reality has no dimensions.

If by “dimensions” you mean extension, yes. But if you mean there will be no space-time, no. If I put blinders over a triangle so that only its corner point can be seen, that would be a dimensionless point, but still a point (and not the absence of a point). The question is, as I move the blinder to the right (along the triangle’s “time” axis), will I find nothing, or will I find something? My argument calculates the odds regarding what you will see.

In this analogy the act of moving the blinder exists in hyper-time, thus it’s only something we do retrospectively (because “in reality” there is no hyper-time, only an instantaneous space-time tube, of some size or shape, among which possible sizes and shapes is, but is not only, a dimensionless point and nothing else). The theist’s argument asks us to put the blinder at the corner point and then asks what we can predict we’ll see to the right of it when we move the blinder, and their argument predicts it will always be nothing. My argument finds that prediction false.

That’s really all there is to it.

Thus:

5. Timelines can only exist if there is a time dimension, so if statement 1 is true there is no timeline. Furthermore, no new timelines can arise because of statements 3 and 4.

This is false. Statement 1 does not say anything about whether there will be a timeline. All it says is what will exist at the first point of time. The corner of a triangle is a dimensionless point. In no way does that entail there cannot then also be a triangle.

The question of whether there will be a timeline is undecided by what exists at the first point of time. That is the point of P2 et al.

And also:

8. I do not believe that hypertime explains how our universe arose. Instead I argue that P1 is false.

This is where you have lost track of my argument. Because I also believe P1 might be false; I even allude to several possible godless explanations of existence if P1 is false. I only grant P1 ex hypothesi, because P1 is the first premise in the theist’s argument against atheism. As I explain in detail at the beginning of the blog post.

10. If no hypertime is needed because the decision is made “instantaneously”, then at the same instant we find “absolutely nothing” and infinite dimensions, timelines, universes. This is a contradiction.

Certainly. In the same sense that the corner point of a triangle, if it is a dimensionless point, cannot also be a triangle. But since I am not making such a ridiculous argument, this is moot, isn’t it?

I am saying that if there is a dimensionless point at ordinal t = 1, then there will be infinite timelines and spaces extending from it, to a probability infinitesimally close to 100%. I am not saying those infinite timelines and spaces will all simultaneously exist at t = 1 (a nonsensical statement).

Thus, I am saying there is no “hyper-time” in which we first see t = 1 alone, and then see t = 1 sitting next to all the timelines and spaces. What you see is instantly what there is. If there is an infinite space-time manifold attached to an empty dimensionless point at the starting corner of it, there will never have been a “hyper-time” in which there was not an infinite space-time manifold attached to an empty dimensionless point at the starting corner of it. There simply will always have been an infinite space-time manifold attached to an empty dimensionless point at the starting corner of it. The odds are infinitesimal that it would have been otherwise, i.e. that there would always have been only an empty dimensionless point and nothing else.

As soon as your definition of ‘nothing’ includes ‘something’, it’s no longer a definition of nothing. Whatever else you might call a state that includes time, it’s not nothing, so the theist will say that it doesn’t answer her argument. No theist need accept your definition of nothing, and all of the arguments attempting to show how a state of timeless nothing cannot exist just confirm what the theist already believes: that it’s nonsensical to say of ‘nothing’ that it ‘exists’, and that it’s an abuse of language to call nothing a ‘state’, given that a ‘state’ (or a set, or whatever) is something, not nothing.

Disagreeable Me’s approach (there is no beginning) smartly avoids the whole ‘something from nothing’ problem in the first place, and seems to me the best way to go.

‘On the alternative notion that there can be a state of nothing in which there is not even one point of time, you get a logical contradiction: a state of affairs that “never” exists.’

By definition ‘nothing’ isn’t a state. There are no affairs. It is no state of no affairs with no time and there’s nothing to exist and no existence. Anything you say to the contrary will be self-contradictory, because ‘nothing’ cannot be, or include, ‘something’, by definition. ‘There is nothing’ and ‘there is one point of time’ are mutually exclusive.

‘…the “nothing” you want there to be, cannot ever have been.’

Well, unless there’s a God, which is the theist’s whole point. But a nothing that in fact is a something cannot ever have been either, because that’s a logical contradiction: a non-state of non-affairs that ‘exists’.

As soon as your definition of ‘nothing’ includes ‘something’, it’s no longer a definition of nothing.

Semantics.

I already address this in the main post. There are many different kinds of nothing. If you pick a kind whose existence is logically impossible, the theist’s argument fails for lack of a coherent premise. I am only discussing coherent arguments. I don’t need to rebut incoherent ones. Their being incoherent already cancels them.

By definition ‘nothing’ isn’t a state.

Semantic legerdemain.

An empty box is obviously a state of a box, distinct from a box with something in it. Likewise, a state of zero energy is as much a state of a system as a state of positive energy. And a state of zero extension is as much a state as a state of extension. And so on. Thus “nothing isn’t a state” is false.

That there is a difference between “there is nothing at t = 1″ and “there is something at t = 1″ fully entails that nothing is a state (because it is a possible state of being at t = 1). Now, if you define “nothing” as that which can never exist, then yes, that will not be a state, because there will never be such a thing. And there never being such a thing already rules out the theist’s premise that there was such a thing. I already make that point myself early in my blog post.

So you have two options: pick a “nothing” that can’t ever have existed (in which case the theist’s argument fails) or pick one that can have existed (in which case my argument proceeds, and the theist’s argument fails). That’s the whole argument of my article in a nutshell.

It seems we have identified the main sticking point. I believe that absolutely nothing implies space-time is 0-D, you appear to believe that it is at least 1-D, or that its dimensionality is undefined. Let’s focus the discussion on this issue.
———————————————

t=0 does not imply there is no time. It’s just a more natural labelling for the first instant of time. The origin of the Cartesian plane is (0,0) not (1,1). The origin of a single dimensional timeline is also 0. t=0 is therefore more natural to me than t=1, but this is an irrelevant side issue. I get that you’re talking about ordinals rather than time units since the beginning.

Now you’re talking in a circle. We’ve been over this. I argue in my blog post that it is logically impossible for there to be absolutely no time.

I’m not talking in a circle. I only appear to be because you haven’t appreciated that I have already demonstrated that it makes sense to talk about there being no time dimension.

Firstly, I don’t accept your argument that it is logically impossible for there to be no time. However, I can skip past that by allowing that there was a single point of 0-D space-time. This point provides both your “when” and “where” for something to exist, without implying that there is a time dimension. As you have agreed that we do not need any dimensions to hold a single point, then it seems natural to conclude that absolutely nothing implies there is no time dimension.

You maintained early in the discussion that you were proving the existence of time only as an example of something that must logically exist and that your argument did not depend on it. Perhaps we should refocus on this issue if this is becoming a sticking point.

More talking in a circle. I already acknowledge the possibility that P1 is false in my blog post. Indeed, that possibility is a major component of my overall argument and I discuss the option several times. You seem to have completely lost track of that fact.

However I assure you I have not. I said this because it seemed to me that you were losing track of the fact when you make statements like “Obviously, the latter is what happened.”. I’m just making the point that you can’t use observation of this universe to reason about what might have happened if P1 is true precisely because we both agree P1 may not be true.

“There was absolutely nothing” implies there was neither a page nor a cube nor a hypercube nor an infinicube, but a single zero-dimensionless point at (ordinally) t=1. But that is a tautology.

I think you’re still not understanding what I’m saying. I’m not saying only that this point existed at t=0, I’m saying that all of space-time consisted of this point.

There can be no other points as there are no dimensions to distinguish between them. This is what it means for a point to be 0-dimensional. If the point exists in 4-D spacetime, then it’s a 4-dimensional point, with any real value for x,y,z and t co-ordinates.

If it’s 0-dimensional, then it has no dimensions at all, or, equivalently, it has values for those dimensions but all the values must equal 0, the same way we can refer to real numbers on the complex number plane as having complex co-ordinate 0 (4 = 4 + 0i). In 0 dimensions, this is the only possible point. There can be no others because there are no legal values for co-ordinates to distinguish between them as the only legal value is 0 if there are no dimensions.

For example, if I form a triangle out of seashells and leave the corner shell off at coordinate x,y = {0,0}, I can say there is nothing at x,y = {0,0}. That in no way entails there are no other shells, much less no triangle.

There is simply no contradiction here.

You are repeatedly misunderstanding me. I’m not saying that there is no “stuff” at t=0. I’m saying there is only a single-point of 0-dimensionless spacetime. There are no other points which could contain stuff. It’s more like saying there is no beach than leaving off one particular corner sea shell.

When I say there is nothing at x,y = {0,0} all I am saying is that there is nothing at x,y = {0,0}. I am not saying if anything else will exist beside it.

No, but if you allow that something may exist beside it, you’re presupposing that there is a place for that thing to exist. In the zero-dimensional model, there are no other places, no other times. You are assuming that there are other times, which is why at the beginning of our discussion I suggested that you need to amend P1 to clarify that a timeline exists. If you believe you have proved the logical necessity of time, you should clarify that your argument depends on this proof and that it is not simply an example of something which may logically exist.

If by “dimensions” you mean extension, yes. But if you mean there will be no space-time, no.

I do not mean extensions. I mean the dimensions that space-time has. Every point must exist in some kind of space. The nature of that space determines how many co-ordinates that point may have and in which directions the point may be extended. There is no reason the space should have any particular cardinality of dimensions. We can reason about 0D, 1D, 2D, 3D, 4D etc all the way up to infinite D. I am assuming that “absolutely nothing” is most consistent with cardinality zero. Which cardinality do you assume?

This is false. Statement 1 does not say anything about whether there will be a timeline. All it says is what will exist at the first point of time. The corner of a triangle is a dimensionless point. In no way does that entail there cannot then also be a triangle.

I believe “absolutely nothing” implies there is no timeline, unless you explicitly state that it does not in your premise. This is why I encourage you to amend P1 to clarify that time exists. The corner of a triangle is not a dimensionless point. It must have at least 2 dimensions (x, y) for it to be part of a triangle. If it was a 0-D point then it exists in 0-D space, and there can be no triangles.

This is where you have lost track of my argument. Because I also believe P1 might be false;

I haven’t lost track of the argument. If you read that statement again you’ll see I deliberately phrased it “I believe…”. What I’m doing here is clarifying my own perspective, not accusing you of believing P1. I just want there to be no misunderstanding: I don’t account for existence with hypertime.

The question of whether there will be a timeline is undecided by what exists at the first point of time. That is the point of P2 et al.

I disagree. If that first point is dimensionless, there can be no timeline. A timeline can only exist if you presuppose it in P1. The first instant is either on a timeline or it is not. This is a qualitative statement about the nature of the first instant.

This is where you have lost track of my argument. Because I also believe P1 might be false;

I haven’t lost track of the argument. If you read that statement again you’ll see I deliberately phrased it “I believe…”. What I’m doing here is clarifying my own perspective, not accusing you of believing P1. I just want there to be no misunderstanding: I don’t account for existence with hypertime.

I am not saying those infinite timelines and spaces will all simultaneously exist at t = 1 (a nonsensical statement).

Are you not? Yet, (with respect to timelines at least) you repeatedly state that they come into existence instantaneously. If this doesn’t mean they exist at t=1, then when do they pop into existence? t=2? But in order to get from t=1 to t=2 you need to presuppose a timeline. You need to assume there is a time dimension. Therefore you can’t have a timeline which pops into existence at t=2. It has to exist at t=1.

Your last sentence proves you are still hung up on hyper-time. You evidently just can’t get passed that.

My last post above already answers your every point. So you should go back and read it more carefully (ditto anyone else following this).

When I say the time dimensions, if they will exist, come to exist instantaneously, I am saying their formation takes zero hyper-time to complete, and thus requires no hyper-time. I am not saying they come into existence at t=anything. They just either exist or they do not. And if they exist, they extend from (ordinal) t=1. And if anything exists that does not necessarily exist, it will not exist at that t=1 but somewhere on the timelines extending from it. And if no timelines extend from it, nothing will exist (except what necessarily exists, which will all exist at the lone point t=1, which is what you are calling t=0).

You also are ignoring me when I keep saying that I am not arguing that P1 is true. I am arguing that if P1 is true, then there will be time dimensions extending from the nothing-point, to a probability infinitely close to 100%. In other words, given nothing decides what will exist, that a nothing point will exist with no timelines extending from it has an infinitesmal probability of existing. The question of whether there was ever a nothing point is wholly separate, and I explain in detail in the original article I am not asserting there ever was. Theists are the ones asserting that.

I’ve saved the most important questions for the end, so you might want to reply to these before replying to the main body of the post to avoid duplication of effort, though you should probably read the main post first.

Your last sentence proves you are still hung up on hyper-time. You evidently just can’t get passed that.

If I can’t get past it it’s because you haven’t explained away the contradiction, beyond asserting that no hypertime is required. Either I’m simply not understand your point or you’re simply not understanding mine. I obviously lean to the second interpretation. I can only try to express myself more clearly in the hopes that you understand me.

My last post above already answers your every point. So you should go back and read it more carefully (ditto anyone else following this).

I have read it carefully. It simply doesn’t seem to appreciate the subtlety of the argument that I’m making. I have explained why with reference to specific points you made, quoting you and articulating as clearly as I can why I do not find your explanations satisfactory.

In particular you have completely ignored what it means for the nothing-point to be zero-dimensional as opposed to being a regular point in 3-D or 4-D space-time.

Rather than telling me you’ve already answered my points, please point out where I’m interpreting them incorrectly or why my own reasoning is flawed.

When I say the time dimensions, if they will exist, come to exist instantaneously, I am saying their formation takes zero hyper-time to complete, and thus requires no hyper-time. I am not saying they come into existence at t=anything. They just either exist or they do not.

This is the critical point where we disagree, so please pay it specific attention
Agreed, time dimensions either exist or they do not. However, P1 says there is absolutely nothing, therefore I think it is reasonable to interpret this as an assertion that they do not exist. Therefore nothing happens. QED.

Now, this is not actually what you mean by P1, as far as I can see. If I understand what you are trying to say by P1, you actually mean “at t=1 (on a timeline), there exists absolutely nothing save for that timeline and anything that is logically necessary”. This is directly implied by your usage of the phrase “In the beginning”, which rather suggests a timeline.

My argument to you is that you should state more clearly that you are presupposing a timeline. But if you do that you are not explaining why that timeline should exist, and so you have not answered why there should be something rather than nothing. So we’re back to my interpretation.

As you yourself have pointed out, if timelines do not already exist as an assumption within the concept of nothingness you propose, then they can never spring into existence. If we allow them to spring into existence, then they would not exist at t=x and they would exist at t=x+1, and this would imply a hypertime, which we both reject. So their existence or non-existence must be asserted in the premises.

And P1 asserts their non-existence.

Your rationale for the necessary existence of time can only account for the existence of a single dimensionless point of space-time. You have not established that a timeline must exist, so please do not assert that you have already proven the existence of a timeline without addressing this argument.

And if they exist, they extend from (ordinal) t=1. And if anything exists that does not necessarily exist, it will not exist at that t=1 but somewhere on the timelines extending from it. And if no timelines extend from it, nothing will exist (except what necessarily exists, which will all exist at the lone point t=1, which is what you are calling t=0).

I agree with the entirety of this paragraph, with the caveat that I believe P1 entails that timelines won’t exist and so t=1 is the only legal time.

You also are ignoring me when I keep saying that I am not arguing that P1 is true.

This is false. If I have given this impression I apologise. I do seem to have got the idea from somewhere (can’t find the quote now, if it even exists!) that you think the explanatory power of your argument does rather suggest that P1 is reasonably likely to be true, and this may have coloured my statements somewhat. However, I assure you that I have not lost sight of the fact that you do not assert its truth and present the argument primarily as a rebuttal to theologists.

What I said in recent posts was that we cannot use this universe as evidence for what might happen if P1 were true because we both agree P1 is false. This was just a reminder because you seemed to be veering dangerously close to this territory. It does not mean that I believed you were asserting P1’s truth.

I am arguing that if P1 is true, then there will be time dimensions extending from the nothing-point, to a probability infinitely close to 100%.

More critical disagreement

I argue that P1 explicitly states that nothing exists. This entails that the nothing-point is not a 4-D point as the hypothetical Big Bang singularity may have been, but rather a 0-D point. If it’s 0-D, then nothing may extend from it as it exists in 0-D space-time.

Pondering what might extend from a 0-D point in 0-D space-time is like pondering how to place four matchsticks so they are all at right angles to each other, or what happened before the beginning of time, or what’s south of the south pole. If we go back to the world tube analogy (say representing the universe as a 2D triangle with the origin at the left and extending towards the present in this shape: <|), then it's like asking what's happening outside the triangle. If the universe were 0-D, then the world tube would be a point. Asking what happens to the right of the point is just as meaningless as asking what happens to the left of it.

Considering what might extend from a zero-dimensional point in zero-dimensional space betrays an incomplete understanding of what it means for there to be no dimensions. You need to assume that dimensions exist in order for your argument to work. As you don't do this, your argument is founded on a presupposition which you seem unable to recognise.

This is demonstrated by your analogy to shells on a beach, which completely and utterly misses my point. My argument is that in a state of nothingness there is only one point, no 2D plane (the beach) on which to place shells, so we can indeed predict that if there are no shells at the single point then there can be no shells at all.

In other words, given nothing decides what will exist,…

Except P1, which explicitly states that nothing exists, and so there are no dimensions within which timelines can extend…

… that a nothing point will exist with no timelines extending from it has an infinitesmal probability of existing.

Or, rather, a certainty of existing, because geometrically no lines can be drawn in 0-D.

The question of whether there was ever a nothing point is wholly separate, and I explain in detail in the original article I am not asserting there ever was. Theists are the ones asserting that.

I get this, honestly I do.

I trust that we are both honest, intelligent and reasonable individuals who are trying the best we can to understand each others arguments, so I am loathe to give up on this exchange. I want to make every effort to understand where you are coming from and to express clearly where I am coming from so that we can finally get to the root of the disagreement and perhaps even come to an accord. I hope you feel the same.

As my replies are rather lengthy, I am afraid you may be skimming over the most critical points. May I ask you a few specific questions? For some of these, your position appears to be clear, but I just want to get it absolutely right. Feel free to give short answers. I just want to zero in on where the disagreement lies precisely. It seems to be related to questions related to time dimensions. We can discuss in more depth later.

1. Do you recognise the distinction between a spatial singularity in 4-D space and a 0-D point in 0-D space?
2. Do you accept that the most reasonable interpretation of “absolute nothingenss” implies that space-time has no dimensions?
3. If no to (2), then why not? Would you say that the number of dimensions is undefined, four or infinite? Some other answer?
4. Do you accept that timelines cannot “spring” into existence without some concept of hypertime?
5. If yes to (4) and they do not spring into existence (they either exist or they do not), then do you agree that the premises should assert whether they exist or not?
6. If no to (5), then why not?
7. If yes to (5), then do you accept that P1 does in fact assert that they do not exist?
8. If no to (7) and yes to (2), how can you account for the existence of a timeline in 0-D?
9. What is your reaction to my rejection of your analogies to cones, world-tubes and shells on a beach, all of which presuppose spatial/temporal dimensions, when I’m arguing that nothingness implies there are no dimensions at all?
10. Do you accept that your defence of the logical necessity of time only proves the existence of a single point of space-time and does not establish the logical necessity of a timeline?
11. Do you accept that nothing can change if there is no timeline?

Rather than telling me you’ve already answered my points, please point out where I’m interpreting them incorrectly or why my own reasoning is flawed.

But that’s just what I’ve already done. Why would doing it again be any more successful?

Case in point…

P1 says there is absolutely nothing, therefore I think it is reasonable to interpret this as an assertion that they [extended dimensions] do not exist.

Yes. At that one moment of time (the “beginning,” if such there was). It says nothing about whether there are other points in time connected to and extending from it. Whether there are is what the rest of the argument proceeds to determine.

My argument to you is that you should state more clearly that you are presupposing a timeline.

If by “presupposes a timeline” you mean “presupposes at least one moment of time,” then yes. And I already do. I’m quite clear about that. If by “presupposes a timeline” you mean “presupposes an extended dimension of time,” then no. P1 says nothing about whether there is a t=2 or not. All it says is that there is a t=1 and nothing is located there (except that which necessarily exists). Whether there is a t=2 (etc.) is then the question that must be answered: if there was nothing at t=1, will there only ever be a t=1 with nothing in it and no t=2 as the theist avers, or not?

If we allow them to spring into existence, then they would not exist at t=x and they would exist at t=x+1.

Can’t you see how illogical this sentence is? Think of it not of time but of the sides of a timeless triangle. You are in effect saying “if we allow a side of that triangle to spring into existence, then the side would not exist at the corner point but would exist at the points extended from it.” How can a side exist at a point? That’s just nonsense. Obviously, being a point, it is not also a line. Obviously the line does not exist at its starting point. It only ever exists on points extending from it. But in no way does that make a timeless triangle impossible. If we put a card over the rest of the triangle, exposing only the one corner point, and ask you, “Given that nothing determines it, do any lines extend from this point, or will it just be this point? And what are the respective probabilities of either?” How would you answer? Think about it.

Thus your final questions are moot. But I’ll answer them anyway:

1. Do you recognise the distinction between a spatial singularity in 4-D space and a 0-D point in 0-D space?

Yes. (Although we should be asking about infinite-D space, since there is no good reason to believe there is only or could only have been a 4-D space.)

That is, unless you mean you cannot have a 0-D point in a nonzero-D space. Every point on this computer screen (which is in at least 4-D space) is a 0-D point, because that is what a point is by definition. A singularity is just a point not surrounded by other points except along one axis (thus singularities can exist at the edges of nonzero-D spaces). P1, if true, basically asserts that there was such a point, it contained nothing (except what cannot not exist), and if anything else exists it extends from that.

2. Do you accept that the most reasonable interpretation of “absolute nothingenss” implies that space-time has no dimensions?

Yes. At the point of time when it is asserted there is nothing. If we are not asserting there is “nothing” anywhere else, then we are not implying there is nowhere else for something to be. Thus, whether space-time has (extended) dimensionally if the first instant of space-time is an empty singularity is an open question. Like that card-covered shape: all you can see is an isolated 0-D point. Can you then infer (as the theist does) that upon lifting the card you will see no lines (no dimensions) extending from it?

3. If no to (2), then why not? Would you say that the number of dimensions is undefined, four or infinite? Some other answer?

As you can see above, you have completely misconstrued questions 1 and 2 so this third question is moot. But it could be reworked to ask: you are looking at that 0-D point and the card covering all else there may be; when the card is lifted, given that nothing determines what you will see under that card, how many dimensions will be there? None? Four? Infinitely many? Some random finite number between zero and infinity? My argument entails it will be some cardinality of infinity. Thus, a multiverse, in which some regions will have all dimensions collapsed (totally or into Calabi-Yau spaces) except three of space and two of time. And those regions will generate the kind of universes familiar to us.

4. Do you accept that timelines cannot “spring” into existence without some concept of hypertime?

No. Because “spring” has non-temporal meanings. I explained this already: when we are talking retroactively about what happened, we (being in time) describe events this way even though from a POV outside of time it isn’t correct (tensed time is an illusion, remember).

Thus on a singularity origins theory we say the universe “sprang into existence” from the Big Bang singularity, but in fact there was no extension of time at the big bang singularity, just a single 0-D point (the Big Bang itself then created all extended time and space), which is essentially the very same thing P1 asserts (except without the infinitely dense energy presumed to be located there, the laws of physics presumed to be there, and so on), and from a POV outside of the time dimension nothing happened, there is just a static universe extending instantly all the way back to a singularity, and always has been, a single eternal 4-D shape. But since we are inside of time, we use the metaphors of temporality, and since these translate into true geometric statements about 4-D shapes, there is nothing wrong with that. Except, evidently, when they confuse people like you.

5. If yes to (4) and they do not spring into existence (they either exist or they do not), then do you agree that the premises should assert whether they exist or not?

They do. You just stumble over the fact that these statements and terms are semantically synonymous…once you understand how all temporal terms translate on B-theory.

6. If no to (5), then why not?

Moot.

7. If yes to (5), then do you accept that P1 does in fact assert that they do not exist?

Moot.

8. If no to (7) and yes to (2), how can you account for the existence of a timeline in 0-D?

Asked and answered.

It is logically impossible for a time “line” to exist at a “point” so your question is nonsense. Whether a time line extends from a point is the only sensible question to ask. And that is the question my argument answers.

You are like someone asking how Big Bang singularity theorists “account for the existence of a timeline at the singularity.” Since their theory neither posits nor requires a time “line” at the singularity, your question is not only irrelevant, but nonsensical.

9. What is your reaction to my rejection of your analogies to cones, world-tubes and shells on a beach, all of which presuppose spatial/temporal dimensions, when I’m arguing that nothingness implies there are no dimensions at all?

I have answered this at least three or four times now. You still haven’t gotten it.

Think, again, about how Big Bang singularity theorists would answer you. You are like someone saying that Big Bang singularity theory presupposes a pre-existing extended spacetime “into which” the Big Bang explodes. But that’s false. There is no spacetime at the singularity (except the singularity itself), and the Big Bang is what expanded that singularity into extended dimensions of space and time. At t=1 there is only one 0-D point; then at t=2 there are several more points of space and one more of time; and so on. If I say there was nothing at the singularity, in what way does that make it impossible for dimensions to extend from it? It doesn’t. But you really aren’t getting this and I am at a loss for how to help you.

10. Do you accept that your defence of the logical necessity of time only proves the existence of a single point of space-time and does not establish the logical necessity of a timeline?

Yes. The proof of the latter is instead what then proceeds from P1, and the finding is that a timeline is not logically necessary but has a probability of existing infinitely close to 100%. It is not logically necessary because it does have an infinitesimal probability of never having been.

11. Do you accept that nothing can change if there is no timeline?

Yes. But whether there is a timeline is precisely the question. The theist asserts not; I prove otherwise, from their own premise.

General Response
Thanks for your patience. I believe we are getting to the heart of it, though you still appear to be misunderstanding me. But take heart! I have noted several instances where we are clearly talking at cross-purposes. If we can sort these out then there is hope for progress.

If we could talk over the phone or on Skype we’d probably sort it out quickly.

When I discuss dimensions, I most emphatically do not mean extensions from a single point (and I have said this). I am describing the nature of space-time itself.

I assert the validity of a concept of nothingness in which space-time itself has no dimensions. Every time I describe a 0-D point, I mean the single unique point that such a space-time could host. I tried to make this clear by referring to the big bang singularity as a 4-D point because it nominally has 4 co-ordinates – (x, y, z, t).

This distinction seems natural to me as a programmer. If I want to represent a point in 2D geometry I use a different structure from that which I would use to represent a point in 3D. The former has two co-ordinate values, the latter has three. In my argument, a 0-D point in 0-D space has no co-ordinate values at all.

The zero-dimensionality of space-time is the most absolute description of nothingness I can conceive of. If this is what P1 implies, then there can only ever be a single point of space-time. From the timeless B-theory perspective of time, there can be no other points in space or time because there are no dimensions within which their co-ordinates can differ from the origin. It most certainly does deny the existence of timelines, because the existence of timelines in zero dimensions is nonsensical as you pointed out.

But this is not how you interpret P1. You interpret P1 as considering a single point in space-time, and then wondering what might be “around” it or extending from it. You seem to assume that this meta-space-time can have either undefined or infinite dimensions.

Infinite dimensions is a perfectly logical construction. Even undefined I can work with: let’s assume there are an infinite number of formulations of nothingness, each with its own particular flavour of space-time. The odds that we will find that we are in one which contains an infinitely high number of dimensions are 100%.

However both postulating infinite dimensions and undefined dimensions seem less like absolute nothingness to me than no dimensions at all. All I’m pointing out then is that you should make your dimensional assumptions clear in your premises, because there are interpretations of absolute nothingness which would deny them.

Specific Clarifications

It says nothing about whether there are other points in time connected to and extending from it.

My interpretation of P1 (space-time is zero-dimensional) is that it does in fact say there are no other points in time.

If by “presupposes a timeline” you mean “presupposes at least one moment of time,” then yes.

No, that is not what I mean. I accept for now your argument that there must be at least one moment of time. I reject that there must be a timeline or time dimension, yet your argument only works if we assume that there are such dimensions. Until you clarify this in your premises, I regard it as a presupposition.

Whether there is a t=2 (etc.) is then the question that must be answered: if there was nothing at t=1, will there only ever be a t=1 with nothing in it and no t=2 as the theist avers, or not?

I think where we differ is that I regard this question as meaningless. We either assume a timeline exists or we assume a timeline does not exist, precisely because we both agree that they do not spring into existence. They either exist timelessly or do not exist at all. Your premises are incomplete because they do not state whether a timeline exists or not.

You cannot start from a premise which postulates a point but does not clarify the nature of the space the point exists in and then make conclusions about that space.

To be facetious for a moment, you’re asking how long is a piece of string. Well, since the string can have any length, it must be effectively infinite.

Can’t you see how illogical this sentence is?

Another misunderstanding. We agree that this sentence is illogical. We agree that timelines do not “spring” into existence. This sentence was serving to clarify and underline this fact by showing how having them spring into existence is illogical. If they don’t spring into existence then their existence or non-existence must be fixed in the premises.

If we put a card over the rest of the triangle, exposing only the one corner point, and ask you, “Given that nothing determines it, do any lines extend from this point, or will it just be this point? And what are the respective probabilities of either?” How would you answer? Think about it.

Classic example of you missing the central point I’m making. I’m asserting that space-time is zero-dimensional for absolute nothingness, and that this implies there can only ever be a single point. I’m not concluding that the existence of a point denies the existence of other points. You couldn’t cover the rest of the triangle with a card because there would be no space for the card or the other points to exist in.

I’ve explained this very clearly with reference to the shells. I hope you understand my objection this time.

Although we should be asking about infinite-D space, since there is no good reason to believe there is only or could only have been a 4-D space.

Neither is there any good reason to believe that we should be asking about infinite-D space. Which is why we must express what kind of space we are talking about. I assert that zero dimensionality is implied by absolute nothingness, because otherwise dimensions (which are not logically necessary) exist.

That is, unless you mean you cannot have a 0-D point in a nonzero-D space. Every point on this computer screen (which is in at least 4-D space) is a 0-D point, because that is what a point is by definition.

This is worth quoting because it is the clearest articulation of our misunderstanding. Please note well that I regard points in 4-D space as 4-D points, because they require 4 coordinates to define them. I accept that you can define a point as internally zero-dimensional (has no width, depth, height or duration), but this is not what I mean at all. I am referring to the position of the point in external space, not to the volume of the space occupied by the point. By this definition, indeed you cannot have a 0-D point in a nonzero-D space.

A singularity is just a point not surrounded by other points except along one axis (thus singularities can exist at the edges of nonzero-D spaces).

Just to note that this definition seems dubious to me and I’m not sure I accept it. If it matters you can probably find a source. But it doesn’t matter to me as I know what you mean by the big bang singularity anyway.

Do you accept that the most reasonable interpretation of “absolute nothingenss” implies that space-time has no dimensions?

Yes. At the point of time when it is asserted there is nothing. If we are not asserting there is “nothing” anywhere else, then we are not implying there is nowhere else for something to be.

But I didn’t say “at the point of time when it is asserted there is nothing”. I was referring to the space in which that point resides. I assert that the dimensions of space-time either exist or do not exist at that point, just as at least four dimensions of space-time exist at the point where I write this sentence. This does not mean they are contained in the point, it just means that at that point you can make a truth claim about whether they exist or not. If it so happens that there are no dimensions, as I interpret P1 to state, then there certainly is an implication that there is nowhere else for something to be.

Thus, a multiverse, in which some regions will have all dimensions collapsed (totally or into Calabi-Yau spaces) except three of space and two of time. And those regions will generate the kind of universes familiar to us.

This is a side issue but it intrigues me. What do you mean by two dimensions of time? It sounds like you’re hinting at something interesting I would like to learn about.

… how many dimensions will be there? None? Four? Infinitely many? Some random finite number between zero and infinity? My argument entails it will be some cardinality of infinity.

Your argument as expressed in the OP concerns itself with what will “spring” into existence. As mentioned many times, “springing” can only happen given a timeline. Timelines themselves must exist timelessly, and so must be assumed to exist or not to exist in the premises or the problem you seek to solve is insufficiently defined. Or, rather, the nature of your argument implies that timelines exist, however this appears to be in contradiction to your premise which states that only the logically necessary exists.

In the card analogy, the card itself implies that the dimensions needed to support other points exist, as the card exists in those dimensions, therefore in the card analogy the premises assert the existence of dimensions.

4. Do you accept that timelines cannot “spring” into existence without some concept of hypertime?

No. Because “spring” has non-temporal meanings. I explained this already:

I know you did. That’s why I encouraged you to write short answers and explicitly stated that some questions were merely intended to clarify points which had previously been discussed.

However, your answer contradicts your previous statement so you have misunderstood the question.

This is what you said previously:

I am not saying they come into existence at t=anything. They just either exist or they do not.

So, the answer I was looking for was “Yes”, because they don’t spring into existence, they “either exist or they do not”, just as you said. I only mentioned hypertime for completeness because they could come into existence if there were a hypertime, but neither of us is assumes a hypertime.

I’m not misunderstanding the nature of time. I interpret “spring into existence” to mean there is some hyper-timeline where our proposed timeline does not exist at t=x but does exist at t=x+1. Both of us reject this. Therefore, both of us should answer “Yes” to question 5.

But since we are inside of time, we use the metaphors of temporality, and since these translate into true geometric statements about 4-D shapes, there is nothing wrong with that. Except, evidently, when they confuse people like you.

It is logically impossible for a time “line” to exist at a “point” so your question is nonsense.

No it isn’t. The question is how do you account for the existence of a line in 0-D. Once again, when I discuss 0-D, I am referring to all of space-time. I am asserting that space-time is 0-D in absolute nothingness, and a line cannot exist in 0-D because this is logically impossible, as you observe yourself.

You are like someone asking how Big Bang singularity theorists “account for the existence of a timeline at the singularity.” Since their theory neither posits nor requires a time “line” at the singularity, your question is not only irrelevant, but nonsensical.

The timeline exists at the big bang singularity. This is not a problem because the big bang singularity exists not in 0-D but in 4-D space-time. I hope you understand what I mean by now.

If I say there was nothing at the singularity, in what way does that make it impossible for dimensions to extend from it?

Because absolute nothingness describes the state where only the logically necessary exists. Dimensions are not logically necessary. If it is true to say at the origin point that dimensions exist, as it is true to say at this point in time that dimensions exist, then we’re not dealing with nothing.

But you really aren’t getting this and I am at a loss for how to help you.

Alternatively, you aren’t getting what I’m saying about the consequences of the zero-dimensionality of space-time. I hope you do understand what I mean by now or I’m at a loss for how to help you! Again, a voice call might be the best bet, as both of us have wasted hours of our lives arguing against positions the other person doesn’t hold simply due to misunderstandings.

I have answered this at least three or four times now. You still haven’t gotten it.

Well, you’ve given three or four different versions of the same analogy. You haven’t explained how any of them apply to the argument that space-time itself is zero-dimensional. You’ve only explained repeatedly how they apply to the argument that there is a point which has no internal dimensions. “You still haven’t gotten” what I’m trying to say. Well, hopefully you have by now.

I disagree with this. I do argue that Big Bang singularity theory does presuppose a 4-D space-time. Note I didn’t say extended. I just refer to a space-time which has 4 dimensions. The singularity is just the pointy end of the 4-D world tube which singularity theorists “presuppose”. But this presupposition is not a problem because scientists are not trying to explain how this space-time which they observe came about, they are instead seeking to describe its geometry.

Some more questions
1. Have I clarified to your satisfaction what I mean by the zero-dimensionality of space-time, in particular that it is not the same as extensions from a point or the internal dimensionlessness of that point? Do you now understand where I’m coming from where previously you did not?
2. Is the interpretation of “absolute nothingness” as entailing the zero-dimensionality of space-time logically coherent?
3. Do you understand now that I assert this interpretation?
4. Do you agree that this interpretation denies the existence of any points other than the origin?
5. Is this interpretation reasonable?
6. Why do you prefer the interpretation that absolute nothingness exists in a space-time of undefined or infinite dimensions?
7. Do you now see where I’m coming from in rejecting your analogies to structures in 2, 3 and 4 dimensions?

The question is how do you account for the existence of a line in 0-D.

I never propose such a thing. At no point in my argument do I declare that the initial nothing point exists in a 0-D space (as you define it). That would beg the question in favor of the theist’s assumption that that is the only place the nothing point could ever exist. The question is whether that nothing point is in a 0-D space or not. And my argument proves not (to a probability infinitely close to 100%).

I know you never define the nothing point in this way. I am quite clear that this is my interpretation of absolute nothingness. I ask you to explain why you prefer your interpretation.

Because dimensions do not necessarily exist.

It is possible to imagine a reality of 0-D. So if we want to assume the most absolute definition of nothing possible, would 0-D not be preferable to undefined-D? Otherwise, the theist can argue that your nothing point is not a nothing point at all, if it allows an unspecified number of dimensions to exist.

If you believe that you are justified in making an exception for dimensions when you otherwise declare that only logically necessary things exist, then you should state it in your premises or prove that dimensions are logically necessary.

You are still missing the point. The theist is saying that if the first point of time contains nothing, then there will be no second point of time. I then examine if this is true. I find that it is not. That is all that’s going on here.

It would be silly to say “if something came from nothing, then there was never nothing to begin with,” since that is a self-contradictory statement. (At best it relies on an equivocation fallacy, using “nothing” in one sense in the if-clause and in a different sense in the then-clause.)

Hence the theist also allows for “dimension to exist” when the first point of time contained nothing: they say God created those dimensions out of the nothing (also instantaneously, BTW). Thus they are not saying “in the beginning was nothing and not even a god could add anything to it, because ‘nothing’ means no dimensions ever exist, and therefore because some do, there can never have been ‘nothing’ and therefore God did not create the world ex nihilo but out of an already-existing extended spacetime.” This makes nonsense of the theist’s argument.

Their argument’s premise is in the beginning there was nothing. Not “there was never ever anything.” The latter is precisely what they have to prove would follow from their premise (that in the beginning there was nothing; from which they conclude, therefore there would only be nothing after that). Otherwise their argument is circular, presupposing the conclusion in its premise (“there would never ever be anything, therefore there would never ever be anything”), and if that’s what they are saying then we can dismiss their argument outright. I do not want to attack a straw man, so I constructed the only non-circular argument possible for their premise and conclusion. The question is then, does that conclusion follow from that premise. My argument proves that it does not. That’s it. That’s all there is to it.

Thus, we are not asking you to imagine an isolated 0-D point and asking whether there will ever be dimensions added to it, since that would be a circular argument, assuming the conclusion (there will never be dimensions) in the premise (there will never be dimensions, as that is what an isolated 0-D point means). No, we are asking you to imagine a nothing point at the start of time and then asking whether there can be dimensions extending from it (like, for example, more time), and how likely that will be. The theist insists that likelihood is zero percent. I find it is nearly 100%.

“An empty box is obviously a state of a box, distinct from a box with something in it. Likewise, a state of zero energy is as much a state of a system as a state of positive energy. And a state of zero extension is as much a state as a state of extension. And so on. Thus “nothing isn’t a state” is false.” – R. Carrier

An empty box is a box, and so it isn’t nothing but something. Being empty can be a state of a box, but being nothing can’t. Nothing can be in the state of nothingness.

The point is that when we discuss absolute nothingness we should eliminate absolutely everything that is not logically eliminable.

An empty box is not nothingness in this sense because it presupposes the existence of a box.

For my argument, this includes a time dimension. Your definition of absolute nothingness also fails because it presupposes the existence of a space-time which has a time dimension (as I will argue in response to your reply to me).

“And there never being such a thing already rules out the theist’s premise that there was such a thing.” – R. Carrier

Quite a few philosophers would object to this that you’re begging the question by presupposing that existence is by definition temporal existence.

“x exists but it never exists” is a contradiction only if it is read as “x exists but it doesn’t exist at all” rather than as “x exists but it doesn’t exist at any time because it doesn’t exist in time”. For example, what’s logically/ontologically impossible about a timeless world whose only inhabitants are the natural numbers, i.e. a plurality of abstract objects?

That’s irrelevant. Again you are losing track of the argument. Theists aren’t arguing from a loose nothing point floating around outside of time. So the existence or non-existence of such a thing is moot. They are saying our timeline begins at a nothing point, and (if god does not exist) must have done so. They are wrong, but that’s not the issue I tackle in detail. I instead analyze what follows if they are right.

They are saying our timeline begins at a nothing point, and (if god does not exist) must have done so.

This quote accounts for why you are implicitly assuming the existence of a timeline for P1 even though you don’t appear to realise it.

But this is not at all how you originally phrased the argument.

even granting the theist’s premise that if there was no God, then there was once absolutely nothing, and therefore there cannot have been a universe, therefore the fact that we are here entails God exists, because our existence would be literally impossible otherwise.

Note that you do not present the theist’s premise as the timeline beginning at a nothing point. Rather the theist’s premise is that the existence of something rather than nothing proves that God must exist. Myron’s universe is a perfectly logically consistent universe and corresponds reasonably closely with my definition of absolutely nothing. This universe has no timeline and so nothing can happen.

I agree with Myron that using the word “never” to prove the logical existence of time is a semantic trick and doesn’t really prove anything.

Although I’m still happy to allow you your one point of 0-dimensional space-time to give you a “when” and “where” for existence to apply.

I posted too soon, I have misread your presentation of the theist’s argument.

You do in fact present the theist’s as maintaining that there was once a nothing point (if there were no God, so I apologise for misrepresenting this.

However you do not establish that they believe this nothing point is on a timeline, and so Myron’s description of this nothing point is valid, and I would argue more valid than yours because the absence of a timeline is more consistent with the meaning behind the question “Why is there something rather than nothing?”. Why should there be a timeline at all?

Since I believe your argument assumes a timeline (as I will continue to argue in response to your reply to me), I do not think it answers this question.

Another point from my point of view is that it is highly questionable whether there are or can be such things as space-, time-, or spacetime-points, which lack spatial or/and temporal extension. It is even more questionable whether there is a possible world consisting of nothing but one of these things. For instance, is there a possible world consisting of nothing but an instant with a duration of 0s? – I don’t think so.
What I think is that instants and 0-dimensional space-points are mathematically idealized (abstract) objects that aren’t and cannot be physically real.
The conception of particles as point-particles, i.e. as 0D objects, doesn’t truly represent physical reality. If spacetime or matter has an ultimate atomic structure, then the fundamental spatiotemporal elements must be minimal phases or stages with a nonzero duration (measured in terms of intervals rather than instants) and minimal regions or bits of stuff with a nonzero extension.

I would be delighted if you could present logical syllogisms demonstrating these assertions. Because those would refute the theists’ argument right out of the gate.

But alas, you seem to be replacing proofs with intuitions. And human intuitions are deeply flawed when it comes to highly abstract questions like this. Especially questions where our experience with reality is likely to interfere. This is why human intuitions routinely fail when dealing with infinities. Our inability to imagine abstract spaces is likewise as easily a product of our brain’s complete inexperience with them, and instead its extensive programming to assume extension of dimensions, in order to navigate the spaces we live in–which ability yet fails again when trying to ponder four or higher dimension spaces, thus illustrating our intuition’s incompetence in these matters.

I’m definitely with Dr. Carrier on this one. You can’t show that any such thing is logically impossible.

It doesn’t matter if there are not mathematically idealized points in the actual world. This world is one of many possible universes. What we observe here is not the only way the universe could be.

Myron, I agree with Dr. Carrier that your intuition is misleading you here.

Now, there’s another question, which is whether that single point of space-time is really the most absolute description of nothing we can conceive of. I argue that it is not unless that space-time has zero dimensions.

Hence the theist also allows for “dimension to exist” when the first point of time contained nothing: they say God created those dimensions out of the nothing (also instantaneously, BTW). Thus they are not saying “in the beginning was nothing and not even a god could add anything to it, because ‘nothing’ means no dimensions ever exist, and therefore because some do, there can never have been ‘nothing’ and therefore God did not create the world ex nihilo but out of an already-existing extended spacetime.” This makes nonsense of the theist’s argument.

You have explained why you are assuming a time dimension. This, despite your dogged resistance to admitting that you are making this assumption up until just now.

I accept your explanation as perfectly reasonable. You are answering an argument put forward by theists in which they assume that time exists. I worry that they may deny that they are assuming time. God might be able to make stuff happen even if there is no time because he’s magic, or other such philosophically lazy hand-waving.

The problem is that your explanation of P1 contradicts your assumption, because you state that only the logically necessary exists, and dimensions are not logically necessary.

I’m coming back to what I said in my very first comment on this. You need to state clearly that you are assuming that time exists and simply explain that this is because the theists assume it exists. You could clarify this by stating unambiguously that you take the word “beginning” to imply a timeline. My problem is therefore not with your argument but with your explanation of it.

I honestly believe that a great deal of time could have been saved if you had read my comments a little more carefully to see where I was coming from. I repeatedly explained why I thought you were assuming a timeline, and you repeatedly denied that you were.

I only make this point because I may want to comment on your posts in future, and I’m hoping we don’t waste as much time in future on a simple misunderstanding like this.

Finally, I just want to confess that for the majority of this discussion I have been under a misconception. I thought that you also sought to provide a possible explanation for why there is something rather than nothing by examining what might follow if we assumed nothing rather than something.

Would you agree that your argument does not explain this because it does not make the most absolute assumption of nothing that could logically be made (i.e. it does not explain why there is a time dimension rather than no time dimension)?

This is just out of curiosity. I’m not saying you claimed that your argument did answer this question.

I hope that the long path towards resolving this misunderstanding has not exasperated you intolerably.

I thought that you also sought to provide a possible explanation for why there is something rather than nothing by examining what might follow if we assumed nothing rather than something. Would you agree that your argument does not explain this because it does not make the most absolute assumption of nothing that could logically be made (i.e. it does not explain why there is a time dimension rather than no time dimension)?

No. Because you still aren’t getting the argument. I aim to explain why there is something rather than nothing if we assume nothing decides which there will be. At no point do I aim to explain why there is something rather than nothing if we assumed there was never anything. That would be self-contradictory. The “most absolute assumption of nothing that could logically be made” cannot be “that there was never anything” because cognito ergo sum. Therefore the “most absolute assumption of nothing that could logically be made” is that there was once nothing (and that it occupied at least one point in time, as otherwise it would never have been). The question then is why it didn’t stay that way but was followed by “stuff.”

The theist’s argument is that “if there was once nothing (and no god), then there would never have been anything.” That is not my argument, but theirs. And they have to prove it, i.e. they need to show that the conclusion logically follows from the premise. So I tested that, and found that that conclusion does not follow from that premise, but in fact a very different conclusion indeed. The theist’s argument then proceeds to “there is something, therefore there was not once nothing (and no god)” and then to “the Big bang entails there was once nothing, but (per previous argument) there can’t have once been nothing (and no god), therefore there was once nothing (and god).” As I noted in the main article, there is more than one thing wrong with this argument, but my article only deals with the first inference, whether “there was once nothing, therefore there would never have been anything.”

One cannot assume “there was once nothing means there was never anything” because that is a premise refuted by present experience and thus it can never be a premise in any sound argument. So theists can’t make any argument out of that. Therefore the only argument they can even attempt is “there was once nothing means only that at one point of time there was nothing.” They then argue there must have been a God or else no timeline would extend from that nothing point. My argument refutes that premise by showing that in any universe with an initial nothing-point, the probability of that universe consisting of only that point is infinitesimal. Infinitely more universes follow that nothing-point with timelines and other “stuff,” all without any god being necessary.

Therefore “if there was once nothing (and no god), then there would never have been anything” is false.

I even said that I understood you hadn’t asserted this, and cleared up that I was asking out of curiosity whether you think this line of reasoning helped to explain why there is something other than nothing.

There is no need to imply that I’m hard of understanding for simply asking for your opinion on the subject.

The fact of the matter is that you have been shown to be incorrect in your explanation of the argument. Specifically, you are wrong on two counts.

1) You have until recently consistently denied that you were assuming time.
2) You argued that only the logically necessary exists in a state of absolute nothingness, and timelines are not logically necessary.

For (1), you have now explained satisfactorily why you are justified in making this assumption, but that doesn’t get around the fact that you denied the assumption for the longest time.

For (2), yes you could argue that we can deduce that there has always been a timeline by observing one now and realising (as I have noted in my arguments) that timelines cannot pop into existence because nothing can do so in the absence of time. This contingency on our observations of time in our universe is not the same kind of logical necessity as you implied in your arguments. It’s empirical in nature rather than a priori.

I am unaware of any mistakes here. You have consistently misinterpreted what I said. I have been consistent in saying it. I only changed the way I said it, several times, in an attempt to help you understand what I am saying. Now you are treating that effort as evidence of being inconsistent. This is starting to turn into a running gag, like “Who’s on first?”

Fair enough. I think the medium is the problem, especially when posts got too long.

I have a sense that you were skimming a lot of my posts without really getting the central point, which is understandable because I know you’re very busy at the moment.

For my part, I spent a very large number of hours going over what you wrote and considering my replies so I doubt I’m misunderstanding you at a basic level.

Anyway, the question has largely been settled in my mind because you appear to have tacitly admitted that you are assuming a timeline by providing a justification for that assumption. I no longer think you’re just completely missing the point, and instead think you could have explained the issue of time a little bit better in your original post.

I can leave it there. It would just be nice to think that you understand why I have a problem with your description of P1 as entailing that “This can only mean that nothing whatever exists except anything whose non-existence is logically impossible.” when it still appears that you tacitly assume that a (non-logically necessary) timeline exists.

Well then I share your frustration that neither of us seem to be able to make the other understand where we’re coming from.

I took your restatement of the theists argument as a perfectly reasonable justification for a timeline, and so I thought that you were actually assuming a timeline.

I know you don’t explicitly assume a timeline, but I think the simple assumption that “stuff can happen” itself is an implicit assumption of a timeline.

The “most absolute assumption of nothing that could logically be made” cannot be “that there was never anything” because cognito ergo sum.

I agree with you that the most absolute assumption of nothing that could have been true of reality would have had to have had a timeline – as the absence of a timeline is equivalent to “there was never anything”. As such, a timeline is logically necessary given what we observe (including the fact that we think and observe at all).

However this is not how I understood logical necessity in your argument. I believed you meant it in a purely a priori sense.

From a priori logic, “there was never anything” is just fine. This may not describe the reality we observe, but it may describe a reality that could have been.

It seems that perhaps this different understanding of the meaning of logical necessity is the source of our disagreement?

From a priori logic, “there was never anything” is just fine. This may not describe the reality we observe, but it may describe a reality that could have been.

I agree. Which gets us right back full circle to where we began: the question is, what is the probability that reality would have been that way, given that there was at least one point in time where nothing was? The Christian argues the answer is 100%. I prove it is near 0%. That’s all there is to it.

You then kept confusing “given that there was at least one point in time where nothing was” with “given that there was once never anything” and the entire thread ensued where I tried repeatedly to get you to understand that these are not the same statements, and that P1 is the former, not the latter. It was only in that process that I had to try and get you to understand what the theist’s argument was, and it is that argument (not mine) that depends on an empirical premise about what now exists. You then confused that as being something I was relying on, even though no such premise exists in my syllogism in the article.

I think you’re misunderstanding me too. You’ve spent at least 90% of this conversation refuting a position I don’t hold.

Which is why a voice chat might be more productive. But perhaps not.

“There was never anything” is a valid interpretation of P1 if a timeline is not assumed or proven. In fact, if a timeline is not assumed or proven, it is the only valid interpretation of P1. If a timeline is not assumed or proven, then nothing comes from nothing.

I’m only getting from “given that there was at least one point in time where nothing was” to “given that there was once never anything” by the attempt to scrupulously eliminate all that is not logically necessary (a priori), as that’s what you indicate we should do.

This includes eliminating a time dimension in my view. Otherwise you’re not eliminating everything. “There was never anything” follows as a consequence of this. This is not a simple misunderstanding of the premise, but a conclusion following from your description of the premise.

So, back to logical necessity. Do you mean a priori logical necessity or only that which is logically necessary given what we observe?

“There was never anything” is a valid interpretation of P1 if a timeline is not assumed or proven.

No, it is not.

This is like saying “a cat” is a valid interpretation of “a mammal.”

I’ve explained why at least five times now. If you haven’t gotten it by now, you never will.

This includes eliminating a time dimension in my view. Otherwise you’re not eliminating everything.

The theist’s argument only requires me to eliminate everything at the first point of time. Whether I must also eliminate all subsequent time is precisely the matter in dispute. It is not the premise of the argument. It is the conclusion. Their conclusion, in fact. A conclusion my argument proves invalid.

Thus, you are invalidly assuming I am “eliminating everything” in P1. Never anywhere does it say that, nor would it make sense to. Because that would produce a circular argument for the theist. And I am assuming they aren’t so stupid as to lean on a circular argument.

Again, I’ve explained why at least five times now. If you haven’t gotten it by now, you never will.

You then confused that as being something I was relying on, even though no such premise exists in my syllogism in the article.

The premise that a timeline exists? Sure there is. And, to paraphrase your words, I’ve explained this to you several times already, but you just don’t get it.

P2: If there was absolutely nothing, then (apart from logical necessity) nothing existed to prevent anything from happening or to make any one thing happening more likely than any other thing.

Nothing existed to prevent anything from happening implies that it is possible for something to happen.

If something can happen, then there must be at least two instants of time. An instant before the happening and an instant after the happening. If those instants don’t exist, then it’s not a happening. Those two distinct instants of time imply a timeline.

Without a timeline, nothing can happen. If you assume that stuff can happen, you implicitly assume a timeline. It doesn’t matter if you don’t state it explicitly. It’s implicit in P2.

Nothing existed to prevent anything from happening implies that it is possible for something to happen.

Right. Somewhere other than the first point of time described in P1. P1 does not mention whether anything else exists somewhere other than that one point. The argument in fact is to determine what will exist apart from that point, if that one point is empty.

The question therefore is, if the point described in P1 is empty, does it necessarily follow that it is alone? The theist says yes. I prove it’s no.

Believe me, I share your exasperation. Please understand, from my point of view, your own words apply to yourself. If you don’t get it now you never will. I’ve explained it again and again and you just don’t get where I’m coming from.

We’re talking past each other. There’s some basic fundamental assumptions that we don’t share. We may root these out or we may have to give up. I’m pretty dogged, and so are you, so this conversation may drag on until we have nothing new to say.

I have thought of one or two new points to make however.

The theist’s argument only requires me to eliminate everything at the first point of time. Whether I must also eliminate all subsequent time is precisely the matter in dispute.

Just to note: I’m tired of artificially saying timelines all the time. Your proof of time may prove a single point of spacetime but does not prove dimensions. I’m just going to say time from now on to mean a time dimension or timeline if you don’t mind. A single point of spacetime is not time in any meaningful sense unless there is a time dimension.

My argument is that your description of absolutely nothing does in fact require the elimination of subsequent time. And here’s why. If you eliminate everything at the first point of time, you also eliminate time itself. Unless you confine yourself to specifying that you are elminating everything except time. Which is fine. But is not how I interpret your original wording.

We can take time out of the question altogether. Time can be viewed as a spatial dimension. Your argument then is to postulate a point at which there is nothing, and then just ask what is there around it, yes? That’s perfectly fine. I have no problem with that.

Until you say that you want to eliminate absolute everything that is not logically necessary. I do not believe that space itself is logically necessary. If there is no space, there can be nothing around this point.

So you’re assuming time/space. And you have a perfectly reasonable justification for doing so. But you don’t realise you’re assuming it. This may be because your intuitions are preventing you from imagining that first point as existing in zero dimensions.

Another interpretation for our disagreement is that I think it is sensible to describe a point as existing in zero dimensions, and that this makes zero dimensionality an intrinsic property of the point, while you possibly think that the number of dimensions in the space surrounding the point is a property of the space and not of the point and so not part of the assumption of that point.

Another interpretation for our disagreement is that I think it is sensible to describe a point as existing in zero dimensions, and that this makes zero dimensionality an intrinsic property of the point, while you possibly think that the number of dimensions in the space surrounding the point is a property of the space and not of the point and so not part of the assumption of that point.

I also “think it is sensible to describe a point as existing in zero dimensions” but the question is: what is the probability that that is what would exist, in the absences of a God. And (as you suspect) I also think “that the number of dimensions in the space surrounding the point is a property of the space and not of the point and so not part of the assumption of that point” (obviously; a point cannot also be a line, and so linearity cannot be a property of a point).

That is why the question is whether, if there is ever a point with nothing in it, that point must necessarily only be “a point existing in zero dimensions” or if it can also be a point connected to other points (and thus be an empty point that is not in zero dimensional space). The theist argues that unless a god is around to make it otherwise, a point with nothing in it must necessarily only be “a point existing in zero dimensions” and cannot ever be attached to other points. I find that the reverse is the case and that it is infinitely improbable that, in the absence of a god (or anything else to decide the matter), that a nothing point will be a zero dimensional point (in your sense), because of all the possible things that can exist for no reason, that universe (a zero dimensional nothingverse) is one single possibility out of infinitely many, and all possibilities are equally likely, therefore a zero dimensional nothingverse has a probability of infinity to one against. Even if there is no god.

Therefore, if a nothingpoint preceded the Big Bang (as the theist argues), we do not need to posit a god to explain why something followed it. The probability that nothing would follow such a nothing point is infinity to one against. And this is not a question of hypertime. It’s a question of the bare probability of what would exist in the absence of anything to decide what will exist.

Your argument then is to postulate a point at which there is nothing, and then just ask what is there around it, yes? That’s perfectly fine. I have no problem with that. Until you say that you want to eliminate absolute everything that is not logically necessary.

I only eliminate “absolutely everything that is not logically necessary” at that point; I then leave unconcluded what might exist apart from that, and proceed to see what the odds are that something would. Nowhere do I say I am positing the complete elimination of everything whatever. That would be self-contradictory. To the contrary, I am asking (just as the theist does), if at that one point there is nothing, what is the probability that that would be the only point that exists?

Note that what then follows is not logically necessary. An infinitesimal probability is still a nonzero probability, thus there was a chance that there would have been only a lone zero dimensional point–it’s just that that chance is exceedingly small, even in the absence of a god. And that’s my argument in a nutshell.

It would probably help to write shorter more focused answers. To that end, I’m not going to address most of your points here, most of which we have already discussed many times.

I believe I already understand your basic argument, so in my view you don’t need to keep repeating it. I get it appears to you that I don’t understand it so repeat it if you must.

I think once again we’re getting closer to the problem.

I’ve explained before that I think points in zero-dimensional space are different from points in 3-dimensional space. O-D points have no dimensional properties, while 3-D points have three dimensional properties (x, y, z values).

A point cannot be a line, as you noted, but this is mistaking the “external” dimensionality I’m talking about, which refers to position in space, for “internal” dimensionality which refers to the extent of a structure internally. How much volume or space it occupies.

By these definitions, all points are internally 0-D. However points in a 2-D universe are externally 2-D, those in a 3-D universe are externally 3-D etc.

For example, in the programming language Java, Point2D is a class (structure) which is used to represent 2D points. It has x and y properties. Point3D is a class which is used to represent 3D points, it has a z property in addition to x and y. This may have influenced why I see dimensionality as a property of a point.

As such, as soon as you consider a point, you should specify its dimensionality. When you say you want to eliminate absolute everything that is not logically necessary at that point, in my mind this includes the dimensionality of the point.

This is simply because in my view the dimensionality of the point is a property of that point and so it has a value at that point. And so I view that point as being zero-dimensional. If the point has 0 external dimensions, the point must exist in a 0D space, meaning there can be nothing around it.

Where I suspect we differ is that you do not view this “external dimensionality” as a property of the point. You view it as exclusively a property of the space, and so it has no particular value at the initially postulated point. In your view, this means it can have any value from 0 to infinity.

As such, as soon as you consider a point, you should specify its dimensionality. When you say you want to eliminate absolute everything that is not logically necessary at that point, in my mind this includes the dimensionality of the point.

But that is a relativistic property. A point’s dimensionality only exists relative to what exists outside of it. If you do not know what exists outside of it, its dimensionality is unknown, yet the point still exists (you cannot tell from the point alone what else exists, if the point is all you see). Thus, we can view the point without assuming anything does or does not exist outside of it. And that is what P1 does. And indeed, that something does exist outside of it is not logically necessary even on my argument. It is entirely a contingency of probability. Thus nothing is assumed to exist at that point except what must necessarily exist at that point. What else may then exist is contingent.

The question is then, what else is then likely to exist? Not “what else necessarily exists,” but what is likely to exist. The theist says, without god, the answer is certainly nothing. I find that without god, the answer is infinitesimally likely to be nothing.

But that is a relativistic property. A point’s dimensionality only exists relative to what exists outside of it. If you do not know what exists outside of it, its dimensionality is unknown, yet the point still exists (you cannot tell from the point alone what else exists, if the point is all you see).

That’s an assertion which I disagree with.

It’s as simple as that. All our pages and pages of discussing this boils down to these two opposing ways of looking at it.

Your viewpoint may be valid, though I’m not convinced of that. I remain convinced that mine is valid, however. So we have two different ideas of what a “point” is. I regard dimensionality as a fundamental property of a point, and you think it fundamentally pertains only to the space around the point.

Quoting wikipedia:

Points are most often considered within the framework of Euclidean geometry, where they are one of the fundamental objects. Euclid originally defined the point as “that which has no part”. In two-dimensional Euclidean space, a point is represented by an ordered pair (x, y) of numbers, where the first number conventionally represents the horizontal and is often denoted by x, and the second number conventionally represents the vertical and is often denoted by y. This idea is easily generalized to three dimensional Euclidean space, where a point is represented by an ordered triplet (x, y, z) with the additional third number representing depth and often denoted by z.

So, Euclid’s definition ‘that which has no part’ appears to agree with you. However the difference in representation between a point in 2D space and 3D space appears to support my interpretation.

Most questions you can ask about points don’t make much sense unless you define the number of dimensions you are talking about.

Is point A equal to point B?

Well, we need to go and compare each of the dimensional co-ordinates of A and B to find out.

How might we arrange 4 points so that the minimum distance between them is 1 unit but the average distance between them is at a minimum?

Well, in 0D the problem is impossible. In 1D they should be arranged in a line, each 1 unit apart. In 2D they should be arranged as the vertices of a square with sides 1 unit long. In 3D (and upwards) they should be arranged as the vertices of a tetrahedron with sides 1 unit apart.

In my view, no mathematical or logical model which asks questions about points is well-defined unless it makes clear what kind of points it’s talking about, 2D points or 3D points or what. In that regard, I do not view your interpretation of P1 to be well defined or coherent.

To refer back to the other discussion about simulation: your P1 cannot be represented on a computer, because to simulate a point you need to simulate a space (if you do not simulate a space you are in effect assuming 0 dimensions), and to simulate a space you need to know what number of dimensions you have. If the number of dimensions are undefined, you can’t simulate anything. Therefore your model is not logically possible (per my view that a priori logical possibility is identical to simulatability).

I suspect we just have to agree to disagree.

My advice to you remains. For the sake of clarity alone you should state that you are assuming that time exists (which you can justify by referring to the original theist argument you are refuting). This resolves the issue by making clear that there is at least a dimension of time. If you want to add a further clarification that you don’t actually think the assumption of time is necessary for the kinds of reasons you have been arguing with me, that’s fine.

My issue is that your original argument seems to be contradictory to those who share my viewpoint.

I regard dimensionality as a fundamental property of a point, and you think it fundamentally pertains only to the space around the point.

This is just semantics. You are basically saying “I am speaking a different language than you and absolutely refuse to read your article in your language, I will only read it as if it were written in my language.”

That’s not a very practical way to argue.

All you have to do is read my article as written in my language, using my definition of terms, and all the problems you cite go away.

This is just semantics. You are basically saying “I am speaking a different language than you and absolutely refuse to read your article in your language, I will only read it as if it were written in my language.”

That’s not a very practical way to argue.

All you have to do is read my article as written in my language, using my definition of terms, and all the problems you cite go away.

No, read again.

I’m not saying “your logic is wrong because I use different semantics than you”.

I’m saying “this is not how I (and presumably others) conceive of a point, so you should clarify your argument.”

I then go on to suggest that the easiest way to do this would be to simply assume a timeline and justify it by referring to the theist’s argument. You would lose nothing if you did this, and would only gain clarity for those like me who think you need a timeline before you can begin to imagine stuff happening.

What we appear to disagree on is whether your argument is unambiguously intended the way you word it or whether as worded it is legitimately interpreted the way I did.

Many, many times I have phrased my objection as pertaining to your wording or description of the argument. Certainly ever since I believed you had justified a timeline by referring to the theist argument.

I also argue that your P1 as you intend it isn’t sufficiently well-defined to reason about. For myself (and I suspect many people), it is not sensible to talk about a point without knowing what kind of space we’re dealing with. An assumption must be made. The most absolutely nihilistic assumption is to assume a space of zero dimensions. Which is why I interpreted your argument differently from how you intended.

I’m saying “this is not how I (and presumably others) conceive of a point, so you should clarify your argument.”

This is still playing language police (only now you are recruiting the undemonstrated premise that more people speak your language than mine).

The bottom line is, you know what I mean now. And on my meaning, everything makes sense. On yours, it does not (as you’ve repeatedly been saying). The correct response to that situation is to stop translating my article into your language and start reading it in the language I wrote it in.

This is still playing language police (only now you are recruiting the undemonstrated premise that more people speak your language than mine).

The bottom line is, you know what I mean now. And on my meaning, everything makes sense. On yours, it does not (as you’ve repeatedly been saying). The correct response to that situation is to stop translating my article into your language and start reading it in the language I wrote it in.

You seem to have something of a habit of misinterpreting what I say. In particular, I certainly never said that more people speak my language. I just mentioned that I presume that I am not alone in my way of thinking.

And I’m certainly not playing language police. I’m simply alerting you to an ambiguity in your argument. You can use whatever language you like as long as it is not ambiguous. Your original argument does not clarify whether time (lines/dimensions) is eliminable when considering absolutely nothing. It’s only clear that they are not eliminable inside your head. You need to communicate that to the reader.

Once again, for emphasis: my criticism now is not primarily with your argument but with how effectively and unambiguously you communicate it in the original post (and much of the subsequent argumentation in these comments).

Furthermore the ambiguity cannot be resolved by realising that one interpretation is contradictory and the other makes sense. I still find your interpretation to be highly dubious because you are attempting to reason about a problem that is insufficiently defined (such as my example how best to arrange 4 points at a fixed minimum distance from each other so that the average distances between them are minimised).

Again, your interpretation seems to me to be like asking how long is a piece of string. It’s too vague to have a sensible answer. The answer you provide is like reasoning that the string must be infinite in length because any length is possible.

This in itself is not a refutation. Your interpretation may be sensible. But it is not self-evidently so to me, so this in itself cannot be used to resolve the ambiguity. A far more reasonable way for the reader to resolve the ambiguity is to suppose that you simply forgot to address the question of whether dimensions exist when formulating the argument.

Finally, I want to raise the point that you are not in fact the person who must define absolute nothingness. Since you are attempting to refute a theistic argument, it is the theist’s interpretation of absolute nothingness that counts.

I can imagine that theists might well agree with me by excluding time in their formulation of absolute nothing. If that is their formulation, then they are absolutely correct to argue that nothing really does come from nothing. Theists, with their highly developed ability to employ woolly thinking and completely disregard reason, might believe that they are justified in arguing that as God is an omnipotent being existing outside time and space, no mere absence of time can limit him from creating whatever he pleases.

If this is the theist’s view, then your whole argument is moot. You must instead argue that God is powerless to do anything without time in which to do it. While I would certainly agree with you here, it’s a harder point to argue robustly due to the incoherency and elusiveness of the very concept of a timeless transcendant omnipotent God.

I can imagine that theists might well agree with me by excluding time in their formulation of absolute nothing. If that is their formulation, then they are absolutely correct to argue that nothing really does come from nothing.

That would be a circular argument. That is a fallacy.

You can’t argue “there is nothing, therefore there was nothing, and nothing comes from nothing (unless there is a God), therefore there would be nothing (unless there was a God); there is something, therefore there is a God” because there is something (so the first premise is false, and contradicts the last premise). So they have to argue “there was once nothing, and if there was once nothing, there would be nothing now (unless there was a God), therefore there would be nothing now (unless there is a God); there is something, therefore there is a God.”

Do you see the problem? (I have explained this to you at least twice already before now.)

The theist cannot start with a premise “there was once nothing, not even time dimensions extending from that nothing” because that would entail there is nothing now. But there is something now, so that premise is known to be false. In other words, if “there was once nothing, not even time dimensions extending from that nothing” then even a God could not produce a universe, because that would require God to add a time dimension extending from that nothing, but the theist has already adopted a premise that rules that out (there are “not even time dimensions extending from that nothing”). Therefore the theist can only adopt a premise whereby it is possible that the nothing-point have time dimensions extending from it (up to now).

The first question then is: is a god the only thing that can make that happen? The answer is obviously no. If a god can do it, then all kinds of other simpler things could, too; but that’s a different rebuttal, which denies the premise that there was once nothing (e.g. it all started with a quantum vacuum or some other brute physical fact), which is the argument I discuss and set aside early in my article, whereas my argument after that explores what follows if we even grant that premise.

So that leads to the second question: do we need anything at all to make that happen? The answer, my argument proves, is no. Even if we have an initial nothing-point, we do not need to assume anything else (not even quantum vacuums) to explain why a time dimension (etc.) would extend from it.

Thus, we are not positing “a state of there never being any time dimension” or any such obvious nonsense that even a theist cannot adopt as a premise (because obviously, if there was ever nothing, there is a time dimension extending from that nothing, so we cannot posit a “nothing” that lacks that; we must instead explain why it has that). Rather, we are just positing, just like the theist must, “an initial nothing-point” which the theist insists must have a God added to it to explain why dimensions extend from it, while the cosmologists point out there are other things, like quantum vacuums, you can add to it that are much simpler and far more scientifically plausible on present evidence that would explain why dimensions extend from that nothing-point–and then I go on to prove that we don’t even need to presume anything is added to it (not even quantum vacuums, no brute facts at all), in order to conclude that probably dimensions will extend from it. Which therefore explains why they do. Without positing anything. Not a God, not a quantum vacuum, not anything. Except the complete absence of anything that decides what will or won’t extend from it. QED.

And I agree with most of that logic, I’m just saying you might want to check with a theist whether their formulation of nothing includes time or not.

“God is magic” circumnavigates a lot of your logic.

This whole issue was raised more or less as an aside. It just occurred to me that you’d need to confirm with a theist.

You completely ignored the important points, namely that you completely ignored the fact that your argument remains ambiguous as originally described, and that many people might find a description of a problem involving points to be insufficiently defined to reason about.

You have also ignored the fact that you misrepresented me as acting as the language police or claiming that the majority of people will use my interpretation.

If a theist tries arguing that there was once a lone nothing-point, with not even time dimensions extending from it, “and then” (a statement now requiring hypertime to be intelligible) there was “a nothing-point, with time dimensions extending from it,” all I need do is direct them to everything you said in this thread as to that being logically impossible and indeed nonsensical.

And no, my argument does not remain ambiguous as described. That you failed to grasp the article’s clear enough exposition is your own failing (proved by the fact that you failed to get it even after half a dozen rewordings and re-explanations, a scale of repetition almost no one I have ever encountered in my life has ever required). That you had to attribute to the theist absurdly self-defeating assumptions in order to get my argument to mean what it didn’t only further points out the irrelevance of your interpretation. If we have to read my words the way you require, then we are straw-manning the theist’s argument. If you want to do that, why not just go straight to the fallacy of straw manning their argument? And once you do that, what is gained by it? A fallacy is a fallacy.

Again, when I say “there was once nothing” it should be self-evident that I am only referring to one point (“once nothing” not “always been nothing”). But instead you retranslated my words with the unusual and inexplicable definition “there was once nothing means there was never anything” and assumed that, therefore, I was arguing “there was never anything, and then there was at one point nothing followed by something” which requires hypertime (the only way to move from the one to the other: i.e. “In the beginning, there was absolutely nothing” without hypertime entails my meaning–as without it no other meaning is possible but that I am speaking only of the starting point of whatever then does exist, and that only that starting point is empty; whereas “In the beginning, there was absolutely nothing” can entail your meaning only by presuming hypertime, which I gave no reason for you to introduce). So you had to introduce something I never did (hypertime) to retranslate my words into your meanings. And only then did any contradictions and problems arise.

You just need more practice at reading what people write as they have written it, rather than radically transforming it in illogical ways never called for, and then complaining at the result.

I semi-concede the point about the theist’s argument. I would just prefer to be clear what that theist’s argument is, as you appear to believe it’s wrong either way of interpreting it.

On the issue of ambiguity: if it’s not your fault that I misinterpreted your original post, then it’s not my fault that you continuously misinterpreted my criticism of your post.

The exasperation you feel at my inability to understand you is mirrored by mine. You didn’t need to repeat your argument. Not once. You only needed to address the problem I had with it. Which took you several weeks and dozens of posts to finally do.

All of your posts about arranging shells or about cones or about 4D universes were entirely irrelevant to my point.

I didn’t finally understand you because you repeated yourself, I finally understood you because you eventually responded to what I was saying about eliminating the time dimension at the nothing point.

I have been doing the hard work here of guessing at what you could possibly mean and suggesting where the disagreement might lie. You have been busy ignoring me and repeating yourself.

When finally the ultimate point of contention was identified (by me), namely that you do not consider dimensionality to be a property of the point, I was left feeling that all of this argument could have been avoided if you had merely addressed the issue of whether time has been eliminated in your post.

This is why I regard your post to be ambiguous, and why I encourage you to clarify this if you intend to rely on the argument in future.

Your characterisation of my interpretation is unfair. It’s not that I interpreted “there was once nothing” as “there was never anything”, it’s that I interpreted “everything which is not logically necessary is eliminated” as including dimensions, because dimensions are not logically necessary.

I only asked you to clarify this point, which you were steadfast in refusing to do.

Your characterisation of my interpretation is unfair. It’s not [a] that I interpreted “there was once nothing” as “there was never anything”, it’s [b] that I interpreted “everything which is not logically necessary is eliminated” as including dimensions, because dimensions are not logically necessary.

That you think there is a difference between [a] and [b] is precisely the problem.

But they are different, Richard. They contain different words which have different meanings.

“There was once absolutely nothing” is too vague to have a precise interpretation. It might mean a vacuum. It might mean a vacuum with no quantum fluctuations. It might mean an empty void with no physical laws whatsoever.

To interpret this in isolation as “There was once never anything” would be unreasonable, which is why I resent your misrepresentation of my position.

But you did provide a definition, in which you were at great pains to stress that everything that could be logically eliminated should be logically eliminated in this picture of nothingness. To me at least (and possibly others), there seems to be no reason to assume that spatial and temporal dimensions are spared from elimination, especially as your nothingness is not well defined without knowing what number of dimensions we’re dealing with.

That there is “never anything” is then a consequence of a literal reading of your definition, not a wilfully contrarian misinterpretation of “absolutely nothing”.

“There was once absolutely nothing” is too vague to have a precise interpretation. It might mean a vacuum. It might mean a vacuum with no quantum fluctuations. It might mean an empty void with no physical laws whatsoever.

Now I know you have lost track of the argument. I am very clear in the article what I mean regarding whether this P1 “nothing” is a vacuum or a vacuum with quantum fluctuations or contains any physical laws whatsoever.

To me at least (and possibly others), there seems to be no reason to assume that spatial and temporal dimensions are spared from elimination, especially as your nothingness is not well defined without knowing what number of dimensions we’re dealing with.

If P1 asserted “there was and never will have been any dimensions” then yes, we have eliminated everything, even all possible futures. But then theism would be false, too. So why would anyone think I was asserting such a ridiculous proposition?

To the contrary, P1 very clearly says there was “in the beginning” absolutely nothing, and in the context of all the explanation and definition leading up to it, it is very clear I mean only the first point of whatever time and space and stuff then happens to follow. It can follow because a God exists (the theist’s claim) or it can follow because a God doesn’t exist (and by his not existing, nothing decides what will follow that first point, because the point itself contains nothing to decide what then comes after it) or perhaps if a God doesn’t exist nothing will follow (the theist is insisting this is logically necessary; I prove it is not, that in fact nearly the contrary is logically necessary), but in all three cases what does follow is not asserted at P1. If it were, then P1 would be asserting that nothing now exists, which we know to be false. So no theist could use such a P1 in an argument for the existence of God. They can only use a P1 that allows something to follow the first nothing point (that’s the only way they can argue that God is necessary for ensuring something does follow–that requires that it be possible that something does, which requires not taking P1 in your sense).

I really don’t know why I have to keep explaining this. Over and over and over and over and over again.

I really don’t know why I have to keep explaining this. Over and over and over and over and over again.

So stop repeating yourself and actually read what I’m saying. You’re repetition is boring and pointless. It’s not going to get us anywhere because it’s ignoring the point.

Now I know you have lost track of the argument. I am very clear in the article what I mean regarding whether this P1 “nothing” is a vacuum or a vacuum with quantum fluctuations or contains any physical laws whatsoever.

No, you have lost track of the argument. I’m discussing possible interpretations of this statement, which you used to portray me as wilfully misinterpreting your point.

The confusion arises not because of this statement but because your explanation in the original post seems to imply that dimensions should be eliminated.

I’m discussing possible interpretations of this statement, which you used to portray me as wilfully misinterpreting your point.

And you are ignoring now what I said in the article. If I clearly state that “nothing” means no X, Y, and Z, and then you come back with “do you mean nothing with X, Y, or Z?” you are clearly disregarding the article. How can you claim the article is unclear, by ignoring what it says and then saying it didn’t say what in fact it said?

“You can’t show that any such thing is logically impossible.” – Disagreeable Me

I very rarely agree with William Craig, but regarding the following general point I do:

“The fact that the argument is framed in terms of metaphysical modality also has an important epistemic consequence. Since metaphysical modality is so much woollier a notion than strict logical modality, there may not be the sort of clean, decisive markers of what is possible or impossible that consistency in first-order logic affords for strict logical modality. Arguments for metaphysical possibility or impossibility typically rely upon intuitions and conceivability arguments, which are obviously much less certain guides than strict logical consistency or inconsistency. The poorly defined nature of metaphysical modality cuts both ways dialectically: on the one hand, arguments for the metaphysical impossibility of some state of affairs will be much more subjective than arguments concerning strict logical impossibility; on the other hand, such arguments cannot be refuted by facile observations to the effect that such states of affairs have not been demonstrated to be strictly logically inconsistent.”

“It doesn’t matter if there are not mathematically idealized points in the actual world. This world is one of many possible universes. What we observe here is not the only way the universe could be. Myron, I agree with Dr. Carrier that your intuition is misleading you here. – Disagreeable Me

Your objection is based on your intuitions, isn’t it? So we may have a clash of intuitions here.
I defend a moderate rationalism according to which rational intuitions have evidential force (under certain epistemic conditions). But I can’t delve into this epistemological topic here.

Why do you agree with Craig in supposing that there is a distinction between logical possibility and metaphysical possibility?

I rather suspect that they are the same, as I can’t think of any reason why they should not be. If they are not the same, then some logically possible descriptions of reality are metaphysically impossible.

What metaphysical laws make them impossible? Why should these metaphysical laws exist?

Just FYI, I agree with Disagreeable Me that the philosophical attempt to invent a new category of necessity (“metaphysical necessity”) as if it were distinct from logical or physical necessity, is bogus. Craig did not do that inventing, though (he just makes use of it); it has a longer tradition in the field (the usual guy appealed to for this is Kripke), but IMO it breaks down on analysis. IMO there are only two kinds of necessity: logical and physical (and usually the latter is not the former, i.e. physical necessities are not usually logical necessities; although they sometimes can be, when that happens we still prefer to call them logical necessities, to distinguish them from physical laws which are themselves contingent but once existent entail outcomes that we call “physical necessity”; and I should mention that some physicists do think all physical necessities are logical necessities, on the premise that there is only one set of physical laws that is logically possible, but none have proven this premise and I am skeptical of it).

“But alas, you seem to be replacing proofs with intuitions. – R. Carrier

Of course, more would need to be said about those claims of mine, and I could say more about them. Here’s one point:

“Elementary particles in the ordinary view of things are point particles. A point can’t have many, many properties. A point is too simple to have properties. However, we know that elementary particles have a lot of properties. They have spin, they have electric charge, they have something called isotopic spin, they have a quantum number called color – it’s not got anything to do with ordinary color – they have generations that they belong to, there are whole catalogs of different kinds of quantum numbers, of different kinds of properties that quarks, electrons, netrinos, or photons have. It sounds unreasonable for a point to have that structure. So the feeling most of us have is that, at some level, if you look deeply enough into things, you‘ll discover that particles aren’t points. That they must have all kinds of internal machinery that gives them these properties.”

That is, it is extremely implausible to assume that 0D objects are substantial enough to be the substrata of different causally efficacious physical properties. Moreover, it seems utterly mysterious how two equally form- and structureless point-particles could have different physical properties. But if particles are 3D objects, then they can have different forms and structures, different shapes, sizes, densities, and they can e.g. pulsate or vibrate differentially (like strings); and then their different properties can be accounted for in terms of such anatomic and dynamic differences.

Fallibility is not the same as falsity. Rational intuitions are not infallible, but this doesn’t mean that they aren’t evidence in principle. The same is true of perceptions; so if fallibility invalidates intuitions, it invalidates perceptions as well.

But when the only property at issue is location, a 0-D point is all you need. That’s why claiming logical impossibility here is fallacious, if you are resting it on irrelevant considerations like these.

Certainly, if you want vibrations and physical structure, you need more. But that is irrelevant to the present question–rather, what we are asking is the probability of there being multi-D spaces for those things to exist in, if nothing exists to decide what will or won’t exist.

Elementary particles may have internal machinery. However it is also possible that they do not.

As far as I’m concerned, anything that can be described mathematically or simulated by a computer is logically possible, and (as I’ve explained in a previous reply) anything that is logically possible is metaphysically possible.

The structure of elementary particles might be mathematical in nature. There’s no reason to assume it’s physical. Susskind might be a brilliant scientist (I’m gradually getting through a series of lectures of his Stanford have made available), and he might be right in his intuition, but even he describes his position as a “feeling”.

If it’s true that “A point can’t have many, many properties. A point is too simple to have properties” then that implies that perhaps it can have some properties, although he appears to deny this in his next sentence.

I do flat out disagree with him when he says “A point is too simple to have properties”. I’m not sure whether he’s really asserting his certainty that they cannot have properties or expressing his doubt for rhetorical purposes.

Now, if they can have some properties, then how many? Where do you draw the line?

Fallibility is not the same as falsity. Rational intuitions are not infallible, but this doesn’t mean that they aren’t evidence in principle. The same is true of perceptions; so if fallibility invalidates intuitions, it invalidates perceptions as well.

Sure, intuitions might be useful. But what Dr. Carrier and I are saying is that they should be held in deep suspicion when dealing with questions like this, and certainly cannot be used to win an argument.

Intuitions might have some evidential uses, but the more you stray outside the bounds of the natural evolved scope of intuition (moderate scales, durations and energies), the more likely you are to be led astray.

Just FYI, there is a problem with the inference “anything that can be described mathematically or simulated by a computer is logically possible.” I used to assume that inference was correct, too. Until I realized it’s a fallacy. I discussed why in my follow up to this post (The God Impossible). But in short, “simulated by a computer” presupposes the existence (and complex architecture) of a computer, which therefore prevents assuming the simulated entity can exist apart from that architecture (or some architecture substituting for it). Likewise “described mathematically” assumes the existence (and complex architecture) of a describer (who is also, in every relevant sense, a computer). We have to take that into account in any inference we draw from the premise that something has been simulated or described.

1)If something is logically possible then it should be possible in principle to simulate it or describe it with mathematics. It doesn’t matter if this is never done in practice.
2)If something can in principle be simulated on a computer or described mathematically, it is logically possible.
The issue of presupposing a computer doesn’t come up here either. Just because something can be simulated on a computer doesn’t mean it has been or ever will be in practice.

In other words, I regard logical possibility as identical to mathematical describability. I do not see how this presupposes a describer or a computer. I assume you misunderstood me.

I agree with 1) and 2). The issue is not either. The issue is that if something can be described/simmed, we cannot infer that it can exist apart from the simulator/describer. The one being logically possible does not entail the other. As I discuss in the follow-up post we are referring to. (You seem perhaps to think I meant something else, I’m not sure.)

If it is possible to simulate particles as structureless points, then it is possible that this is a true description of particles.

That’s all I was saying. I’m not asserting that it must be true for some universe, which is I believe how you interpreted it.

However, I think I also disagree with your larger point. I will at some point get around to getting into that issue on your other post (which I had already read, but didn’t have time to answer as I’ve been concentrating on this argument).

If it is possible to simulate particles as structureless points, then it is possible that this is a true description of particles.

That’s what I mean is a fallacious inference. We cannot infer from “it is possible to simulate particles as structureless points” the conclusion that “it is possible that this is a true description of particles” (I’m not saying the latter is false, only that the inference is invalid).

This is more evident if you try to build a proper syllogism to get that conclusion from that premise. It won’t work, without relying on a false or unprovable premise.

If particles can be simulated as structureless points, all you’ve proved is that they can be simulated as structureless points. You can not proved they can be structureless points.

This is because a sim sneaks in tons of additional information about those “structureless points” and hides it in the logic registers of the computer running the sim. Without that information, the sim doesn’t work. That means if you have particles as structureless points, they won’t behave the way they are being simulated, for lack of all that hidden information. Which means they might not even be able to exist without that information, which has to be stored somewhere–usually in the structure of the particle. Hence, “structureless particle” might be a self-contradictory statement as Myron suspects.

Now, this does not mean it is self-contradictory, or impossible. Only that we cannot infer the contrary from what we can simulate. Because simulations always involve simulators; real particles don’t have those on hand.

Let me make clear why I even bring up computer simulations. Computer simulations cannot be contradictory or ambiguous. The act of simulating something irons out any ambiguity or contradiction in your model.

You could not simulate a model where electrons are heavier than protons, protons are heavier than neutrons and neutrons are heavier than electrons, because there is a contradiction inherent in it. Therefore this is not logically possible.

I think any model which is free of contradictions or ambiguity is possible for some universe. Any such model which is consistent with our observations is possible for our universe.

(Although, you should be aware that “computer simulations cannot be contradictory or ambiguous” is strictly-speaking false: analog computers can be both, human brains being the most common example, and even digital computers can run fuzzy logic routines that generate considerable ambiguity, and contradictory sims are produced all the time: they are what cause software crashes. But I understand your point: if we design and program a computer a certain way, and define a sim as a program that will actually run, then it can be true, for that computer system, that “simulations cannot be contradictory or ambiguous.” But you still have to have the computer. That creates a problem when you try to infer that what you simulate on that computer can exist apart from that computer.)

You haven’t explained how you can believe that anything which can be simulated must be logically possible (statement 2) above) but not believe that simulating particles as points shoes that this is logically possible. I can’t make any sense of this. I assume that you misinterpreted statement 2)?

This is because a sim sneaks in tons of additional information about those “structureless points” and hides it in the logic registers of the computer running the sim.
…
Because simulations always involve simulators; real particles don’t have those on hand.

Note that I’m not quite denying that points are structureless. Just to be clear, I’m denying that they must have physical structure. They may have structure in a mathematical sense, and this would be compatible with them being modelled as points with properties.

The idea of physical structure at that scale is something I find to be quite naive. Physical structure is something that only exists at larger scales. At that scale, I suspect that our notions of physicality do not apply (as hinted by Quantum Mechanics).

I also find the idea that the universe must store information somewhere to be quite naive.

If the information in the real universe must be stored somewhere, then where? Where is the speed of light stored? The grativational constant? If a point contains structures analogous to registers, where is the information describing the state of those registers stored?

After all, the state of computer registers are stored in atoms and particles. As you seem to argue that atoms and particles can exist without the equivalent of physical internal registers to store their properties, then let’s say they do have registers. Now those registers require a substrate to store their properties, just as computer registers do. And so on ad infinitum.

Positing an internal structure doesn’t explain anything. Some more basic level would be needed to sustain that structure, unless you’re willing to accept that some stuff just have properties without those properties being stored anywhere in particular. Either it has to continue to more and more levels of finer structure ad infinitum or it has to stop at some level, at which you have basic points having properties. Either is possible.

If you don’t want turtles all the way down, it has to stop at some level. At some level, there exists stuff that has properties but no physical structure.

I know. The question is whether (a) it is logically possible that they don’t have physical structure (but still have distinguishing properties) and whether we know (a). I am saying we cannot know whether (a) is true if all we have is the premise “particles without physical structure (but with distinguishing properties) can be simulated.” That premise does not lead to (a) by any logically valid argument. Because whether such particles can exist outside a computer is always going to be the begged question.

If the information in the real universe must be stored somewhere, then where? Where is the speed of light stored? The grativational constant? If a point contains structures analogous to registers, where is the information describing the state of those registers stored?

Superstring theory (for example) answers all of these questions. The answer is in the shape (structure) of spacetime. Each particle is an undulating (“vibrating”) knot in spacetime, its properties derived from its geometric shape and how that shape interacts with other shapes. For example, spin is a ripple (a wave) in space-time that is rotating in a Calabi-Yau dimension rather than in our familiar spatial dimensions. And because such spins can only exist in a limited number of coherent modes (resonant frequencies), that is why spin only exists in fixed units (anything else produces an incoherent string vibration, which ceases to be observable as a particle–which is also why virtual particles exist, as random wiggling sometimes realizes particle modes for fleeting instances, and only when a fleeting mode becomes enduring, by creating a resonant vibration, do we end up with a non-virtual particle; and so on).

IMO there has to be some answer, otherwise nothing would exist to fix (for example) the speed of light. If nothing exists to cause c, then c will not be fixed, it will vary randomly. Conversely, if c is fixed (as we observe it is), then something must be causing it to be “that” and not “something else” (something that is itself fixed). Can that “something” be immaterial (like some sort of mystical Platonic whatsit)? That’s what my article The God Impossible questions the wisdom of. Such a notion is not actually as intelligible as we think (and citing our ability to imagine it doesn’t work, precisely because of my point that we can only imagine it because we are doing it on a simulator, called a human brain, which means we aren’t really imagining an immaterial thing, but a material thing simulating an immaterial thing, which begs the question of whether the immaterial thing could exist apart from that).

Now, as it happens, c is caused by Planck’s constant h, which is caused by the smallest spacetime unit measurable (a Planck length and a Planck time), by the simple physical fact that the fastest possible speed is the smallest unit of space crossed in the smallest unit of time, and the fact that as one approaches that speed, spacetime starts curving in on itself and the time dimension disappears (i.e. at c, all points in time are collapsed to the same point, and consequently time stops and no time exists to continue accelerating in). That’s why when we use natural units, c disappears. It does not exist anymore as a constant. In natural units (when we measure space in Planck lengths and time in Planck times), c = 1, h = 1, and G (the gravitational constant) = 1. Anything multiplied by 1 is itself, so the constants disappear from all the equations of physics. In natural units, for example, E = m. Not e = mc^2. The only thing “c^2″ is doing in the equation is to convert the result into human units of length and time.

In Superstring theory, what causes the Planck units to be what they are is that at that scale, things fall into other dimensions than the ones we live in (the Calabi-Yau spaces), and as those are curved in on themselves, things that do that, just loop around and pop right back out again. That quantizes everything (e.g. we can’t make a ruler that can measure a space smaller than the Calabi-Yau manifold, it’s geometrically impossible because a ruler is always made out of Calabi-Yau manifolds). The physical structure of spacetime thus causes h, which in turn causes c, which in turn causes G. The only way to change c, h, or G is to change the physical structure of spacetime. And here is where physicists start to suspect that other values for c might be logically impossible, since every possible spacetime structure ends up with the same observed c, because c is a function of h and h is a function of the smallest unit of spacetime, so whatever that smallest unit is, still h = 1, and c is then measured in those units and becomes 1 as well, so it is logically impossible to have any other c…if Superstring theory is true and is the explanation of the properties of particles.

For example, if we changed the Planck length in this universe, we’d never notice, because rulers are all made of Planck lengths. For instance, a ruler that is 10^100 Planck lengths will remain 10^100 Planck lengths no matter what a Planck length is, so we will never notice a change in what a Planck length is. The only way to make any observable difference on Superstring theory is to eliminate all calabi-yau spaces (so that there is no Planck unit), but that produces impossible universes (subject to infinite forces and thus dimensional collapse).

It’s thus an intriguing theory. And that’s not the only reason why.

This also does not lead to any infinite regress. The “bottom” turtle is simply the structure of space-time. You need go no further.

I know. The question is whether (a) it is logically possible that they don’t have physical structure (but still have distinguishing properties) and whether we know (a). I am saying we cannot know whether (a) is true if all we have is the premise “particles without physical structure (but with distinguishing properties) can be simulated.” That premise does not lead to (a) by any logically valid argument.

No, that’s not the question at all. We actually agree on this point.

I never meant to give the impression that I believed that particles had to be simple points. I agree with you 100% that that premise does not lead to such knowledge. Instead I’m making the case that that premise leads to the possibility that they are simple points.

I brought up the issue of simulation to attempt to explain why it is possible, and then you contradicted me saying that this inference was invalid.

Just FYI, there is a problem with the inference “anything that can be described mathematically or simulated by a computer is logically possible.”

You’ll notice the inference you were contradicting states “logically possible”, not “logically necessary”.

I never meant to give the impression that I believed that particles had to be simple points. I agree with you 100% that that premise does not lead to such knowledge. Instead I’m making the case that that premise leads to the possibility that they are simple points.

And I never once argued you were saying “that particles had to be simple points.” I have consistently been arguing against the “the possibility that they are simple points.” Or rather, against the claim that we can know this is possible from the premise “we can simulate it.”

In other words:

P01. We can simulate structureless point particles with distinguishable properties (spin, mass, etc.).
P02. ???
C03. Therefore it is logically possible that particles are structureless point particles with distinguishable properties (spin, mass, etc.).

There is no true premise (P02) by which you can get conclusion (C03) from premise (P01).

C03 is therefore not established by any valid argument. We therefore cannot assert P03 when given only P01.

Just a quick note that your spiel about the fundamental constants is interesting, but I’m only skimming it for now as it’s of only peripheral relevance for what we’re talking about.

I’m not sufficiently well educated on theoretical physics to be able to answer many of your points. And so I allow that you may be correct in most of what you say.

However the fact that there is a fine tuning debate at all suggests that the values of at least some of these constants could change in ways which would be perceptible to us. Perhaps c was a bad example.

There are configurations of the constants for example that would not allow stars to form. This information must be stored somewhere.

I can kind of see why you might suppose that strings are in themselves structures that could somehow encode properties in a way that points or not and so perhaps it’s not turtles all the way down. I’m not 100% convinced, but I’ll accept that your argument is plausible. I still suspect that the strings might have properties like momentum or vibrational frequency which your argument would demand need storing at some lower level.

Conversely, I don’t see any logical problems with conceiving some fundamental elementary particles as just having properties that are not stored anywhere in particular.

But since you seem to allow that that may be true of particles anyway, I’m not sure why we’re arguing about it.

There are configurations of the constants for example that would not allow stars to form. This information must be stored somewhere.

I concur.

And one of the main tasks physicists set for themselves is figuring out where that information is stored.

So far, they’ve gotten it down to two things: particles (and their properties) and (the structure of) spacetime. From these two facts, all known physical laws can be deduced. Superstring theorists believe these all collapse into just one thing: (the structure of) spacetime.

Time will tell if they are right.

Conversely, I don’t see any logical problems with conceiving some fundamental elementary particles as just having properties that are not stored anywhere in particular.

This is the relevance of our other thread about the fallacy of the simulation thesis. That you can “conceive” of something is not sufficient evidence that it is possible. Because you can only conceive of it on a machine (your brain). Thus, we cannot know if it can exist apart from a physical structure. To adapt the language, the particles you are conceiving do not have “properties that are not stored anywhere in particular,” because their properties are stored in the circuits of your brain. Therefore, you are not in fact conceiving of particles with “properties that are not stored anywhere in particular” no matter how much it might seem to you that you are. You just can’t see the circuits of your brain. That you cannot see them (or the necessity of them for your ability to conceive of anything) misleads you into assuming they aren’t necessary. But that assumption is fallacious.

This is why “argument from conceivability” is a very dubious mode of argument indeed. Except when we can establish a transfer of concept to reality (by analyzing what exactly is needed for each element and seeing a way to replicate it in some other substrate–in this case, the properties of particles stored in the circuits of your brain: if they are stored in some other way, then certainly the model can possibly be transferred from imagination to reality, but notice how this asserts what you were previously denying, the need to have those properties stored somewhere in particular. So is there a way to get that same inference to work, without assuming the transfer of data storage from one medium to another? Not that I can conceive. Nor can we ever conceive of one, even in principle, since all conception requires a machine. This does not entail that it is logically impossible, since it is a limitation on what we can compute, but it does entail that we cannot know if it is logically possible, precisely because we are incapable of modeling anything without a machine to do the modeling).

I still suspect that the strings might have properties like momentum or vibrational frequency which your argument would demand need storing at some lower level.

Strings are not things separate from spacetime. They are structures of spacetime itself. They certainly do have “properties like momentum or vibrational frequency”…and they are stored in the shape of spacetime itself. Vibrational frequency is literally just a series of humps or twists in spacetime: warp spacetime a certain way, and you get a “vibration” (a literal, physical wave…and a wave of space, not in space). Nothing else is needed. That’s the last turtle.

Momentum is more derivative. The momentum of a photon, for example, equals (Planck’s constant)(speed of light)/(wavelength), and “wavelength” is (on string theory) a physical structure of spacetime (an actual geometric wave pattern with an actual length). Planck’s constant and the peed of light are just unit converters, both equal to 1 when we convert all units back to the natural unit, the smallest actionable size, which is the Calabi-Yau dimension (a physical structure of spacetime, with a physical size, equal to the Planck length and the Planck time). Thus the momentum of a photon equals 1/(wavelength), which is simply f, the frequency of the photon (the number of physical bumps per unit of time), which is nothing more than a shape, a shape of spacetime itself. That’s the last turtle.

(Note that in reality a photon is a spiral rather than a bumped line, but still it’s a shape, whose frequency simply describes one physical curl per x units of space; and on string theory, the photon exists only because this spiral rotates back around on itself like a closed loop, hence a “string,” but it does this using more dimensions than the ones familiar to us–on string theory there are at least seven other dimensions of space, which are curved back in on themselves and have a total circumference equal to or in the ballpark of the Planck length, too small for us to see them or notice our movement around in them, although we all occupy them all the time, it’s just that our bodies extend into them a distance much smaller than a single electron, because that is as far as those dimensions extend.)

P01. We can simulate structureless point particles with distinguishable properties (spin, mass, etc.).
P02. ???
C03. Therefore it is logically possible that particles are structureless point particles with distinguishable properties (spin, mass, etc.).

There is no true premise (P02) by which you can get conclusion (C03) from premise (P01).

P0.1 That which we do not know to be contradicted is possibly true (Note: by possibly true I mean we have no reason to believe it is definitely false – it could be that you have a different interpretation)
C0.1 Therefore that which is internally logically consistent and consistent with our observations is possibly true
P0.2 That which we can simulate is internally logically consistent
P01 We can simulate structureless point particles with distinguishable properties (spin, mass, etc.).
C0.2 Therefore point particles are internally consistent
P03 Point particles are consistent with our observations
C03 Therefore point particles are possibly true

The adamantium plane analogy doesn’t work because it isn’t consistent with our observations of the world.

P0.1 confuses epistemic with logical possibility. Many logically impossible things are not known to be logically impossible to us. Therefore we cannot infer from epistemic uncertainty that something is logically possible. I discuss this very problem in detail in The God Impossible. That makes C0.1 an equivocation fallacy.

(C0.1 also does not follow from P0.1. C0.1 contains terms and expressions not found in P0.1 and you provide no other premise by which to derive those terms and expressions from P0.1. That makes this a fallacy of non sequitur as well. But the equivocation fallacy is the more important error being made.)

P0.2 conceals a hidden premise: the only reason that which we can simulate is internally logically consistent is that its consistency is realized across microcircuits (or neural nets). That therefore begs the question if the logical consistency will remain when you remove the simulator (the substrate). For example, a computer screen is not outer space. It’s a computer screen. Thus anything you can display or animate on a computer screen is only able to be so because of the underlying system of registers and causal interactions in the computer itself. Take those away, and you won’t get that display or animation at all. Thus we cannot infer that what is being displayed or animated on that screen can exist apart from the logic gates, registers, and electron placements that causes it to be displayed/animated (or something else that can stand in for what they make logically possible).

C0.2 therefore does not follow from P0.2/P01 unless you grant my very premise.

You are therefore turning P03 into another equivocation fallacy: in your syllogism it now conflates “point particles apart from a simulator” with “point particles on a simulator.” Because at no point have you established that P0.2 can remain true without the assumption of the underlying computer system. Therefore that fact must commute to P03. So the only valid conclusion would be P03(corrected): Computer simulated point particles are consistent with our observations. And that means C03 is invalid unless you correct it to C03(corrected): Therefore computer simulated point particles are possibly true. Which is a trivial conclusion (no one disputes C03(corrected) is true, and C03(corrected) tells us nothing about what can exist apart from a simulator).

I’m making the epistemic claim that he can’t know this. I even stated clearly that we may have different meanings of possibility here and said explicitly that I’m only talking about what we can know, so you’re accusation of equivocation is absolutely unjustified.

Again, you appear to be arguing against a straw man.

There may be plenty of things that we may not know are logically possible, but insofar as we can simulate something, we know that something is not inherently (logically) impossible a priori.

If our observations do not contradict something, we should judge it to be possible in fact.

I regard the concept of an adamantium plane as logically possible (in the a priori sense). We know it is not physically possible (a posteriori) in this universe because there is no adamantium in this universe.

But you’re just trapping me into a conversation about the meaning of words. I’m not really interested in that conversation right now.

I just wanted to make the point that simulating point particles in a computer demonstrates there is no inherent contradiction in that model of reality. If the simulation behaves according to our observations of the universe, we have no right to claim to know that this model is not accurate.

You seem to be arguing against something else completely.

I’ll attempt to break it down again. You’ll have to cut me some slack if I don’t form my argument 100% correctly according to the rules of philosophy. I’m not a philosopher. I trust that you can use your human ingenuity to somehow understand where I’m coming from nonetheless.

Premises/Definitions:
P1:That which is logically possible (by which I mean there is no a priori reason why they could not be true) is that which does not contradict itself.
P2:That which is simulatable on a computer is not self-contradictory. (Note 1, the behaviour of the computer must match the model – if the computer crashes, then that must be considered part of the model that is not self-contradictory) (Note 2: I have a feeling that this premise could be broken down into a simpler argument but I’m not going to here).
P3:That which is epistemically possible (by which I mean that which may be true as far as we know) is that which is consistent with our observations and is logically possible.
P4:Point particles are simulatable on a computer.
P5:Point particles are not contradicted by our observations.
Argument:
A1. By P4 and P2, point particles are not self-contradictory.
A2: By A1, and P1 point particles are logically possible.
A3: By A2, P5 and P3, point particles are epistemically possible, by which I mean that point particles could be an accurate model of particles as far as we know.

Now, I recognise you have a problem with P2, but I don’t agree with you at all and I’m probably going to save that argument for the thread on the God Impossible. But I think you’ve already granted some interpretation of P2 already when you said “I grant all that.” in response to my post arguing for the identification of “simulatability” with “self-uncontradictedness”.

Perhaps some of this could be cleared up by putting this another way.

I only want to claim that we do not know that point particles are impossible (which is what Myron claimed). In normal language, I would think this means they are possible, however you may mean some more fundamental meaning whereby “possible” and “impossible” are not the only options, there is also “maybe possible”.

If you want to say that I have only shown that point particles are “maybe possible” and not that they are “possible”, then fine, split that hair if you must.

I only want to claim that we do not know that point particles are impossible (which is what Myron claimed). In normal language, I would think this means they are possible, however you may mean some more fundamental meaning whereby “possible” and “impossible” are not the only options, there is also “maybe possible”.

And you are right, I would agree with this much more modest thesis. But it is much more clearly stated as: we do not know whether structureless point particles are logically possible.

And we could add to that that, so far, it has been impossible to imagine such a thing. For the reasons noted upthread: properties need to be stored somehow, and structure is the only storage medium we have ever empirically observed to exist, and we have no way of imagining structureless storage. Therefore the burden is on anyone who claims such a thing even can exist, much less does.

And this is where you might be slipping into the immodest thesis. Citing against the claim that “we have no way of imagining structureless storage” the fact that “I can imagine them / I can simulate them on a computer” would be a logically fallacious objection. Because “I can imagine them / I can simulate them on a computer” is strictly speaking false: you aren’t really imagining/simulating structureless points, because to imagine/simulate them you are storing their properties in a structure (the brain/computer). We know of no way to imagine/simulate anything without a physical structure to store the data in. Therefore we cannot use the premise “I can imagine structureless points / I can simulate them on a computer” in any argument whatever. Such a premise is at present always false.

Granted, we don’t know if it is merely contingently false or if it is false because such a thing is logically impossible. But that is what gets us back to the point: we do not know whether structureless point particles are logically possible.

(They may well not be. And I suspect they are not. For the same reasons I suspect God is logically impossible, even though we have yet to prove it: read, again, The God Impossible. But you’re right, that’s a separate issue.)

I do also subscribe to the immodest thesis, but that was never my intention here. Some confusion may have arisen because we have different meanings for “logically possible”.

By logically possible, I mean the rules of logic do not prohibit a certain proposition, model or argument from being true a priori. I think by this particular meaning we do in fact know that point particles are logically possible.

I’m not sure what you mean by logically possible, but it very much appears to me that you mean metaphysically possible, a concept we both defined to Myron as being equivalent to logically possible.

This is because you are assuming some metaphysical premises which may prevent something which is logically possible (my meaning) from being metaphysically possible. One such premise is
“properties need to be stored somehow”.

I put it to you that that is a bald assertion. I think that like Myron you are allowing your intuition to lead you astray.

The universe may no more need storage to remember its state than it needs a cause. You can’t reason from what we observe in the universe and naively apply it to the universe itself. Just because computers running simulations of physical systems need storage does not mean that physical systems themselves need storage.

Even if I allow that your metaphysical assumption may be true, then point particles remain logically possible (my meaning). They’re just not metaphysically possible. They are only logically impossible given your metaphysical assumptions.

It seems to me that you, like Myron, are drawing a distinction between the two kinds of possible that we have no reason to believe exists save for intuition.

Your claim that imagining structureless storage is fallacious is itself fallacious in my view. I’m using storage to run the imagination, but in the imagined model there is no storage. That’s what the sentence means. The brain is not part of what is imagined. The only point that imagining them makes is that they are logically consistent and thus logically possible (my meaning). I agree that it doesn’t prove they are metaphysically possible.

But if you are suggesting that structureless points are impossible simply because we can’t imagine them or simulate them without employing structures, then I have to say that’s a ridiculous point of view, and so I assume this is not your implication. Just in case it is, I would point out that we are similarly incapable of imagining or simulating strings without employing structures, and you seem to have no problem with that.t

By logically possible, I mean the rules of logic do not prohibit a certain proposition, model or argument from being true a priori. I think by this particular meaning we do in fact know that point particles are logically possible.

But if we do not know whether “the rules of logic do not prohibit a certain proposition” then we cannot say that that proposition is logically possible. And the fact is, we do not know whether “the rules of logic do not prohibit the proposition” that there can be structureless particles with distinguishable properties. Thus you can’t say whether they are logically possible or not.

All the evidence we have (including sims) are structure-dependent (e.g. when you simulate structureless particles, their properties are still stored in a structure: whether microcircuits or neurons; thus you have not, in fact, simulated structureless particles).

Yes, I likewise reject a third category of “metaphysical possibility” (there is only logical and physical possibility) but this is distinct from epistemic possibility, which is merely an expression of uncertainty, not actuality. It is possible I am wrong that 1+1=2; but that does not in any way mean it is logically possible that 1+1=3. It is possible Fermat’s last theorem is false (because I do not know how to develop or check the proof of it). But that does not in any way mean it is logically possible that Fermat’s last theorem is false.

Epistemic uncertainty compels us to conclude either “it is (to some extent) probable that x is logically possible,” or “it is (to some extent) improbable that x is logically possible,” or “I do not know whether x is logically possible,” depending on the information available to us. And in this case, we have no information from which we can infer that structureless particles are logically possible, and plenty of information suggesting they might not be.

I’m using storage to run the imagination, but in the imagined model there is no storage. That’s what the sentence means.

Then that would make that sentence false. In other words, saying “in the imagined model there is no storage” is false, because there is storage (the information is being stored in neurons). You are simply denying established facts if you maintain the information isn’t being stored. You are then, in effect, replacing reality with a cognitive illusion: “it doesn’t seem to me that the information is being stored, because look, I’m imagining it without storage” is just to succumb to the cognitive illusion of not seeing the neurons that are doing the storing, and then treating that illusion as if it were reality. If you can only imagine a model without storage using storage, then you are not proving the possibility of realizing the model without storage.

The brain is not part of what is imagined.

But it is necessary for what is imagined (physically? certainly; logically? possibly). That’s the point. For example, “I am imagining a structureless electron with a charge of -1″ is impossible unless you have neurons storing the information “that electron has a charge of -1.” Therefore you cannot argue from “I am imagining a structureless electron with a charge of -1″ to the conclusion “there can be a structureless electron with a charge of -1″ because your ability to imagine such a thing was impossible but for storage of the very information you are trying to get to exist without storage.

In other words, the fact that simulators must use structure to code the model prevents us from ever actually simulating structureless information. We can deceive ourselves into thinking we are, by ignoring the fact that the information is really being stored in a structure and could never have been imagined if it weren’t being so. But that’s willfull ignorance. Not logical argument.

The only way that rules of logic can prohibit anything is to demonstrate a contradiction. The fact that we can simulate point particles and that this simulation behaves as we expect proves that this model in itself contains no contradictions. You have allowed this.

Therefore, by my definition of logical possibility, point particles are certainly logically possible.

Your examples of 1+1=3 and a false Fermat’s last theorem only serve to illustrate my meaning. It is not possible to simulate or describe a world in which these false beliefs are true. It is possible to simulate a world where point particles are true, so they must be logically possible.

Then that would make that sentence false. In other words, saying “in the imagined model there is no storage” is false, because there is storage (the information is being stored in neurons).

Missing the point again! Notice the word “in”. The storage is most certainly not in the model. The storage is outside the model. The storage is not part of the model. The model itself assumes no storage. We only need storage to calculate or imagine the consequences of the model. How many ways do I need to say this before you understand me?

Yes, the mere act of simulating something does not prove that it can exist independently of the simulation. It proves only that the simulation is logically possible, not metaphysically possible. If there are no fundamental metaphysical laws (as I believe), then logical possibility and metaphysical possibility are the same thing. If there are metaphysical laws (i.e. state is impossible without some form of physical storage), then logical possibility is not identical to metaphysical possibility.

A couple of examples to illustrate why your argument about storage as applied to point particles is so misguided:

Do you believe that the digits of pi in the decimal representation must be stored somewhere? That’s a lot of information, it must require an infinite amount of storage. After all, whenever we calculate pi, we must use storage in order to perform the calculation! The same is true for calculating Pi in other radices.

You also believe that string theory strings are not dependent on storage. And yet like pointless particles and like the digits of pi, we still need storage in order to imagine them or reason about them. This fact seems to tell us nothing whatsoever about whether they can exist without some more fundamental substrate. It’s irrelevant. It has nothing to do with the question.

And the same is true for point particles.

To show that point particles are metaphysically impossible, you need to introduce a new premise. This premise is that all state requires physical structure. Unless you can prove that this is so, this is just an arbitrary intuitive assumption. It may be true, but in that case it is a metaphysical law, and you are postulating a difference between logical possibility and metaphysical possibility.

A model of point particles which assumes this physical law is logically impossible. A model which does not assume this physical law (such as my proposed simulation) is logically possible.

You really are positing a difference between logical possibility and metaphysical possibility, at least according to my interpretation of these terms. If you disagree with this then you must have some other interpretation in mind. Please explain.

The only way that rules of logic can prohibit anything is to demonstrate a contradiction. The fact that we can simulate point particles and that this simulation behaves as we expect proves that this model in itself contains no contradictions. You have allowed this.

That’s false. I’ve explained repeatedly why it is not a valid conclusion. Simulations depend on structure. Therefore no sim can ever prove anything can exist without structure. It’s a logical impossibility–unless we can construct simulators that themselves have no structure, but whether we can do so begs the very question being asked.

It breaks down like this:

First, there are countless things that are logically impossible that we do not know the demonstrations of. Therefore, there are things that we don’t know are logically possible. You must admit this.

Fermat’s last theorem was one such thing for hundreds of years: no one could simulate it one way or the other, so no one knew whether the figure described by the theorem was logically possible or not (and for your information, no sim could ever test it and none ever has, because it is a statement about an infinite series, and that would require an infinitely long computation–until we get sufficiently powerful quantum computers running, but we don’t have those yet; it was proved not by simulating it, but by syllogism).

Only when a proof was created and multiply vetted did we know that Fermat was right: the figure his theorem describes (a shape corresponding to a^n + b^n = c^n for any n larger than 2) is logically impossible after all. But no one knew that until recently. Thus, before this century, that it was logically impossible wasn’t known (although it was suspected for good reasons, but that does not amount to a proof–although the validity of that suspicion supports my point that we can likewise have valid suspicions about point particles without yet having proofs, and indeed that’s the whole point of my article The God Impossible).

Second, that we can simulate a structureless electron does not permit the inference that structureless electrons can exist outside a simulator, and all known simulators are structured, therefore simulated electrons are never in fact structureless.

Denying this is only to wallow in naivety, as if pretending computers are immaterial. In actual fact, the electron’s properties can only be sustained by being stored in a material (the microcircuits); take away that material, and you cannot simulate a structureless electron. Thus we cannot infer that structureless electrons are possible, when we can only make them possible by smuggling in electron structure (by hiding it inside a box on the table and pretending it doesn’t exist).

Do you believe that the digits of pi in the decimal representation must be stored somewhere?

Yes. The digits of pi are a human invention. There are no actual digits of pi beyond those we compute (and being computed, they are stored somewhere). If you mean potential digits of pi, rather than actual ones (i.e. what the digits would be when we compute further out), those digits are stored as the equation for computing pi (which is stored in computers, human brains, physical books, etc.). There is no way around this.

Of course, “digits” are themselves human fabrications (there are no digits in circles, just quantitative relations; digits are just letters in a human-invented language). We made digits up as a way to represent the reality, which is a certain ratio between a circle and its radius, which is arbitrarily defined (we decide what “circle” and “radius” mean) but nevertheless real (circles and radii exist apart from humans).

Circles and radii exist, and thus are stored in, space itself: all of space is a storage medium for all the axioms of geometry which entail the properties of space, such as circularity; and for axioms of geometries of spaces that don’t exist, those, insofar as they actually exist, are stored in human minds, and, insofar as they potentially but do not actually exist, are stored in spacetime as potential computations of potential minds (or computers), just as spacetime itself exists as a potential expansion of any initial space-time point: potential at that point, actual at any other time-point after it.

There is, in short, nothing that actually exists that is not stored in some medium (such as spacetime or particle structure), and nothing that only potentially exists is relevant here (potential electrons do not exist), except insofar as we want to know what is required to make a potential thing actual (what is required to make a potential electron into an actual electron), which is precisely the question at hand: do we need structure to do that or not? Sims can’t tell us.

But I’m not positing that they’re running. Actually, running the simulation is completely beside the point. All that is necessary for a simulation to prove the logical possibility of a model is for an algorithm to be possible which will simulate that model. It never needs to be run. That’s all I’m saying.

The fact that it is possible to write algorithms which will simulate particles as points proves that there are no inherent contradictions or ambiguities in this model, and therefore it is possible that this model is true.

That’s all I’m saying.

(Although, you should be aware that “computer simulations cannot be contradictory or ambiguous” is strictly-speaking false: analog computers can be both human brains being the most common example

No, you misunderstand me. There is nothing ambiguous about the algorithm running in the brain, because there is nothing ambiguous in the laws of physics that govern the brain. If brains make mistakes and behave unpredictably that’s because the algorithm is not perfect and highly complicated/chaotic.

Now if you believed in free will, you might have in the brain an example of a computer which is ambiguous.

and even digital computers can run fuzzy logic routines that generate considerable ambiguity, and contradictory sims are produced all the time: they are what cause software crashes.

Poppycock! I’m a computer scientist so I’m on home turf here. You’re perhaps not wrong, but you are at least misunderstanding my meaning.

Fuzzy logic is not ambiguous. For a given input, a given output will be determined. Determinism is a subset of what I mean by unambiguous or uncontradictory. Any algorithm which is deterministic must be unambiguous. You will get the same results every time.

But even stochastic algorithms are unambiguous. If the algorithm states 50% of the time you get heads, and 50% of the time you get tails, then this is neither ambiguous nor contradictory. It’s perfectly well specified.

An example of an ambiguous/contradictory algorithm would be to state that you get heads 100% of the time and tails 100% of the time (while never getting both heads and tails at the same time). This sentence is false. A square circle.

You can’t simulate these on a computer or describe them mathematically, because they aren’t really algorithms. They are vague pieces of English which do not describe a well-defined concept.

Finally, software crashes are not caused by contradictions. They are caused by a number of different things, none of which are contradictions the way I intend the term.

1) The program detects an event or state which was not anticipated by the programmer and the program runtime terminates itself for safety
2) The program attempts an operation which is not allowed by the operating system, and the operating system terminates it
3) The programmer has decided the best thing to do is to crash as something prevents the program from behaving as intended.

You might argue these are contradictions, but that is not how I intend the word. If there is a contradiction between what the program wants to do and what the OS allows it to do, the contradiction is resolved by the OS overriding the program. In fact, you could argue that this is perhaps true of many crashes. Therefore crashes support my point. Crashes prevent ambiguity or contradictions. You just have to consider crashes to be part of the algorithm.

As such, any computer simulation algorithm describes a model which is consistent with itself. If a model is consistent with itself, I don’t understand why it is not a possible model for some universe. Much like the argument you make in this article, what metaphysical laws could there be to prevent such a model being possible?

I grant all that. The relevant point is that all of that still requires a physical computer.

Thus we cannot infer that anything we run on a physical computer can exist apart from that (or from some comparable substrate). Equations cannot float free of any physical reality. They are descriptions of a physical reality (potential or actual). Thus you need some physical reality to describe, for what the equation says to be true.

That’s why an equation describing the heart as a pump cannot pump blood. You still have to have the thing itself doing that. That we can simulate an animal, with no heart, whose blood is pumped by magic, does not mean such an animal is logically possible–apart from a physical system creating it (in this case, the computer). Thus, that we can simulate it, does not permit the conclusion that it can exist–outside a machine that creates it.

There are two relevant premises here:
1)A simulation proves that some model is possibly descriptive of reality
2)A simulation proves that some model is necessarily true (perhaps elsewhere in the multiverse?)

As it happens, I believe in (2) as a consequence of the Mathematical Universe Hypothesis, and (2) is what you’re arguing against here.

But that’s not the point I’m making in this thread. I’m just stating (1). You appear to have misunderstood me as I’ve argued in a previous post.

There are two relevant premises here:
1)A simulation proves that some model is possibly descriptive of reality
2)A simulation proves that some model is necessarily true (perhaps elsewhere in the multiverse?)
As it happens, I believe in (2) as a consequence of the Mathematical Universe Hypothesis, and (2) is what you’re arguing against here.

Not at all. I have been consistently arguing against (1). [I would never assume anyone would assert (2). Least of all a programmer!]

A simulation does not prove “that some model is possibly descriptive of reality.” Because a simulation entails a long series of hidden premises (all the data and circuitry), which when removed (as by removing the simulator) might make the simulated model logically impossible to realize.

Thus, being able to sim something only proves that you can sim it. It tells you little to nothing about whether it can be realized outside the sim.

The only way you could use a sim to reach a conclusion about possibilities in reality is if you can map every necessary component of the sim onto some real thing, such that removing the sim leaves everything in place to realize the model. For example, we can simulate an airplane made of Adamantine[TM], a completely invincible, unbendable material with zero thickness and mass. But that does not mean Adamantine[TM] is a logically possible material. Because the sim can only realize Adamantine[TM] by having the substrate to realize it (circuits and commands, realized in a physical system that is not made of Adamantine[TM]). Take away that substrate, and no Adamantine[TM]. You have to replace that substrate with something, all the things necessary to make Adamantine[TM] possible without the computer simulator architecture underlying it. And whether that is possible is precisely what the sim itself does not tell you.

(Although you could in principle design an elaborate sim that did that; but this becomes a circular argument, and thus is limited in what it can prove, e.g. we have to have prior knowledge of the existence or logical possibility of every required element of the necessary substrate, then we can infer from (a) the sim, combined with (b) prior knowledge of the existence or logical possibility of every required element of the necessary substrate, whether (c) the simulated entity can exist outside the sim.)

The problem is most obvious in the case of consciousness, where consciousness is a sim, thus to suggest it can exist apart from a simulator is prima facie self-contradictory; and this cannot be gainsaid by saying we can imagine consciousness apart from a simulator, because we can only imagine consciousness apart from a simulator by using a simulator, which means we are not in fact imagining consciousness apart from a simulator. But this illustrates a flaw in the entire general inference from “we can simulate it, therefore it can exist outside the sim.” That rule of inference is simply invalid. It therefore cannot be assumed true in any other case, either. For example, “we can imagine structureless point particles apart from a simulator” is false, because we can only “imagine structureless point particles apart from a simulator” by using a simulator. Thus we are never in fact imagining structureless point particles apart from a simulator. We therefore need some additional knowledge to conclude that structureless point particles can exist apart from a simulator, knowledge the sim by itself cannot provide.

If particles can be simulated as structureless points, all you’ve proved is that they can be simulated as structureless points. (Richard Carrier)

Therefore you allow (at least contingently) that they can be simulated as structureless points.

2) If something can in principle be simulated on a computer or described mathematically, it is logically possible. (Disagreeable Me)

I agree with 1) and 2). (Richard Carrier)

Thefore you allow that particles are logically possible.

What you deny is that they can exist without structure. This is claiming that they are not metaphysically possible.

I do not claim that simulating point particles proves that they are metaphysically possible. I claim that it proves that they are logically possible.

I assert the premise that logical possibility is the same thing as metaphysical possibility (which means that there are no metaphysical prohibitions beyond logical possibility). I do not prove this. Only if this premise is granted does it follow that point particles are metaphysically possible.

You are jumping from the proven logical possibility directly to the unproven metaphysical possibility (while still calling it logical possibility) without acknowledging that I am simply asserting rather than proving that logical possibility implies metaphysical possibility.

However you have also made this assertion.

I can only interpret your continued misunderstanding of the argument as a reluctance to backtrack and contradict your earlier agreement with me that logical possibility and metaphysical possibility are the same thing.

(I’m going to ignore for now your argument that simulations only prove something can exist with structure, just as you ignored my argument that the structure is outside the scope of the model being simulated. I also find your statement that the digits of Pi do not exist until they are calculated to be very strange. I’ll get back to this stuff later, I just want you to focus on the main point I’m making here.)

The latter is too ambiguous to be useful. Can an infinite spiral staircase exist whose stairs increase in size according to Fermat’s quadratic? The answer is no, because such a shape is logically impossible (the description of such a shape is internally inconsistent/entails contradictions). But we did not know that (for sure) until recently, even though we suspected it for hundreds of years. Does that mean such a staircase was “metaphysically” possible in those centuries? No. It was always impossible. And when we didn’t know that, we simply didn’t know whether it was possible or impossible. Full stop.

If metaphysical possibility is not just a useless synonym of logical possibility, then all it can possibly refer to is a subset of logical possibility. That is, some things are logically possible that are not metaphysically possible, but nothing is metaphysically possible that is not logically possible. But since we’re only concerned with whether structureless point particles are possible either way, it doesn’t matter if they are metaphysically possible, all that matters is whether they are logically possible. If we can’t establish that, we can’t establish any other kind of possibility for them. So “metaphysical possibility” is a useless term here.

So that’s all we are concerned with when we ask whether structureless point particles can exist: are they logically possible? Period.

That it is logically possible to simulate x only proves that it is logically possible to simulate x. It does not prove that x can exist apart from the simulator. That would require some additional premise. And that is what is lacking in any attempt to go from “we can simulate structureless point particles” to “structureless point particles can exist outside of a simulator.”

The point that sometimes we don’t know whether something is logically possible or not is wholly irrelevant. By my meaning of the word (which I have repeatedly clarified), then we do know that point particles are possible.

The distinction between logical possibility and metaphysical possibility is useful, and the latter is certainly not too ambiguous to be useful.

You yourself repeatedly distinguish whether something can be simulated (i.e. logical possibility, i.e. no logical contradictions, well-definedness) with whether it can exist (outside of the simualtor) (i.e. metaphysical possibility).

It is no more ambiguous than when you discuss whether something can exist outside of a simulator. It is just a label for this question.

Your example of a spiral staircase is both logically and metaphysically impossible because metaphysical possibility must be a subset of logical possibility, specifically those logically possible models which are not contradicted by some metaphysical law or other.

What we are discussing is whether point particles can exist. This question is metaphysical possibility. Logical possibility is demonstrated by the simulation. Nowhere do I claim simulation proves metaphysical possibility unless you accept the premise that logical possibility is equivalent to metaphysical possibility.

You yourself repeatedly distinguish whether something can be simulated (i.e. logical possibility, i.e. no logical contradictions, well-definedness) with whether it can exist (outside of the simualtor) (i.e. metaphysical possibility).

Then you still don’t understand what I am saying. Because that is certainly not what I am saying.

That something can be simulated does not establish logical possibility. It only establishes the logical possibility of the simulation (and as it happens, also the physical possibility of the simulation–which is what you seem to mean by metaphysical possibility, although I’m not sure; I am following the meaning of that term as developed by Kripke, whereas you seem to be conflating metaphysical and physical possibility, and it’s wholly unclear to me what you think the difference is between logical, physical, and metaphysical possibility).

Whether something simulated can exist when you take away the structure (the simulator) is then a question of either logical possibility (does the existence of such a thing entail contradictions? I am saying we don’t know one way or the other, yet have reasons to suspect the answer is yes) or physical possibility (which is a subset of logical possibility: to be physically possible is to conform to known physical laws, e.g. flying to Mars in a fourth spatial dimension is logically possible but not physically possible because it just so happens that Mars is not connected to the Earth by a fourth physical dimension; likewise, traveling faster than the speed of light might be logically possible, but due to the laws of physics it just so happens to be physically impossible; etc., so whether point particles are physically possible is a question of whether, for example, we could ever make such a thing within the constraints of the actual physics of this universe, and that’s a narrower question than whether they are logically possible).

You still can’t get the point that a simulated point-particle is structure-dependent and therefore not really an example of a point-particle. You are deceiving yourself into thinking it is by ignoring the fact that every simulation is structure-dependent and therefore can never test whether structureless properties can exist. Simulating them thus does not prove they are logically possible. Full stop.

You seem to still be confused about what definitions I’m using for my terms, so, I’ll give my definitions again.

Logical possibility: That which is well-defined and self-consistent. No contradiction can be derived from the proposed axioms. (We do know that point particles are logically possible because no contradiction can be derived from a system of axioms which would model particles as points).

Examples:
1. If Socrates is a man, and if all men are mortal, then it is not logically possible that Socrates is not mortal.
2. It is logically possible that each electron has a rest mass of one kilogram.
3. If we observe and measure that electrons do not have a rest mass of one kilogram, and if we assume that each electron has a single well-defined mass, then it is logically impossible that each electron has a rest mass of one kilogram.
4. It is logically possible that electrons are point particles because we find no contradictions when we examine this possibility.

Metaphysical possibility: That which can exist or happen in some possible world. This is a subset of logical possibility where what is possible is constrained by the addition of some additional axioms known as “metaphysical laws”.

Examples:
1. If there is a metaphysical law prohibiting state without structure, then point particles are metaphysically impossible
2. If there is a metaphysical law prohibiting time travel, then time travel is impossible in all possible worlds

Physical possibility: That which can exist or happen in our universe. This is a subset of metaphysical possibility where what is metaphysically possible is constrained by the additional axioms known as “physical laws”.

Examples:
1. It is not physically possible to send a message faster than light
2. It is not physically possible to have an arbitrarily accurate of both the position and momentum of a particle
3. It is not physically possible for an electron to have a rest mass of one kilogram.
3. It may or may not be physically possible for particles to be structureless. We don’t know.

I hope that clears that up.

The rest of your argument is moot because you didn’t understand what I’m saying.

Your examples of metaphysical laws are just physical laws. Or else they are laws of logical possibility. One or the other. There is no difference otherwise. And thus this middle category of “metaphysical possibility” doesn’t exist.

That it is logically possible to simulate x only proves that it is logically possible to simulate x. It does not prove that x can exist apart from the simulator. That would require some additional premise. And that is what is lacking in any attempt to go from “we can simulate structureless point particles” to “structureless point particles can exist outside of a simulator.”

Agreed, apart from the “lacking” bit, because the supposedly missing premise is “logical possibility is the same thing as metaphysical possibility”.

Which has been clearly stated and agreed already, although it seems we must have different interpretations of these concepts.

Definition 1: That which is logically possible is that which is well-defined and self-consistent
Definition 2: That which is metaphysically possible is that which can exist in some possible world

Premise 1: A computer simulation represents something which is well-defined and self-consistent
Premise 2: Anything that is logically possible is metaphysically possible
Premise 3: It is possible to write a computer simulation representing point particles which produces behaviour that agrees with our observations of particles (note that the structure of the computer system is not part of the model that is being simulated, it is external to it)

Argument:
A1: From premise 1 and definition 1, a computer simulation represents something which is logically possible
A2: From A1 and premise 3, point particles are logically possible.
A3: From premise 2 and A2, point particles are metaphysically possible.

Conclusion: From definition 2 and premise 3 (agreement with our observations), it is possible that our universe is a possible world in which particles might be structureless.

Discussion:

Our disagreement arises for two reasons
1) You are not recognising the distinction between logical possibility and metaphysical possibility as concepts. Sure, we might have different language but I have repeatedly provided the definitions I am using and you have more or less ignored them.
2) You are implicitly assuming that Premise 2 may be false by postulating a metaphysical law “That which has state must have physical structure to store that state”

Hence, simulating point particles does not prove they can exist independently. To make that conclusion, you need to adopt premise 2, which I feel is reasonable, and which it appeared to me that you were doing when you agreed with me that logical possibility and metaphysical possibility were the same thing.

Again, “Premise 1: A computer simulation represents something which is well-defined and self-consistent” is only true of the computer, not the simulation. There is nothing “well-defined and self-consistent” except when we include the registers storing the data regarding the properties of the particles. Take away those registers storing that data, and do we have a “well-defined and self-consistent” simulation left over? No. (No simulation is then physically possible.) So the next question is, at least in principle, could we have a “well-defined and self-consistent” simulation left over? That’s precisely the question we can’t answer this way.

Is a particle with properties not stored in any structure logically possible? A computer simulation can never answer that question. Where the data is stored is part of what makes a simulation “well-defined.” That the data is storable is part of what makes a simulation “self-consistent.” Take away the stored data, and can you still have a simulation of a particle with defined properties? No. The properties have to be stored somewhere. Is a particle with properties that are stored nowhere “self-consistent”? That is precisely the question we have yet to answer, and cannot answer, even in principle, by running a sim on a computer.

Is a particle with no structure at all capable of having different properties than another particle with no structure at all? Is that even a meaningful question? Can it be “well-defined” without resorting to structure? (i.e. without storing the differences between these two particles in a structure–like a microcircuit) Can it be self-consistent to say that two particles that have no physical differences (being structurally identical), nevertheless have physical differences (having different properties)? Can it be made self-consistent only by adding to the particles some data stored in some other structure (like a circuit register)?

So I am not concerned with any distinction between logical and metaphysical possibility. I am only concerned about logical possibility (thus your disagreement number 1 does not exist). And I am not assuming the possibility of a metaphysical law. I am assuming the possibility of a logical law: that it might in fact be logically incoherent to have a structureless particle that is (a) different from another structureless particle or that indeed has (b) any physical properties at all (e.g. a structureless particle can never even in principle collide with another, having zero volume). We do not know if this is logically incoherent. But neither do we know it is logically coherent.

Thus we do not know if structureless particles can satisfy your Premise 1. Therefore your argument is unsound (having an undemonstrated premise–and a premise you can’t demonstrate except by circular argument, presuming the possibility of structureless simulations in order to argue for the possibility of structureless simulations).

Thus, your argument doesn’t work the way you want it to:

A1: A computer simulation represents something which is logically possible.

This can be taken in two ways, either as:

A1(i): A computer simulation is something which is logically possible. [Which premise I grant, since computer simulations exist.]

Or as:

A1(ii): A computer simulation can represent something which is logically possible independent of the computer. [Which makes your argument circular: you are presuming the conclusion in the premise. This form of A1 is precisely the thing we do not know is true.]

If we continue with A1(i), all we end up with is A3(i): Computer simulations of point particles are metaphysically possible. Which isn’t the conclusion you need. So how can you get from any other version of A1 to the version of A3 you actually need? You can’t. Not by any presently known argument, all of whose premises are known to be true.

You can’t just drop the word “represents” and pretend it means the same thing as “is.” And that it is possible to represent point particles is not equivalent to point particles being possible apart from the representation. Because possibly A1 is only true if X is present (a computer); and possibly P3 is only true if X is present. But that would mean A2 is only known to be true if X is present. Therefore, point particles are only known to be possible if a computer is present (doing all the work of making them possible).

Likewise your Premise 3 doesn’t work as written, since the possibility of writing a program does not entail the ability to run it. Can a computer program run of itself, without any computer or any physical analog whatever? That is precisely what we don’t know. It certainly looks like it’s a no (we’ve never seen such a thing, and it certainly looks inconceivable).

A computer program is a set of instructions that refers to structures (circuits or their analog, or to other programs that refer to circuits or their analog, but that reduces to the same thing). Any program that didn’t refer to any such thing (that never once refers to where information about the particles will be stored, for example) would not be logically possible (or rather, running it would not be possible, since the program of itself would be meaningless, containing no actionable instructions that would ever result in a simulation).

Maybe you can write a program that refers the information to be stored in the structureless particles being simulated, but that is precisely what we do not know to be possible (and there is certainly no way to write such a program known to us, as if simulated objects could themselves store information that is not being stored anywhere in the computer itself, a notion that would drive Alice in Wonderland bonkers).

Thus, that computers can simulate x in no way proves that x can exist apart from computers. All it proves is that x can exist as the process of a computer.

You’re kind of missing the point. Bit of rewording might be required. Precedence of the “is possible” operator might be confusing you.

P3 can be reworded as “exists” to avoid confusion. Let’s just assume I’ve written a computer simulation of point particles, rather than muddying the possibility issue by claiming that it is possible to write such a computer simulation.

“simulation” is the predicate that a simulation exists to simulate the parameter
“consistent” is the predicate that the parameter is logically possible, in the sense that it is free of logical contradictions and so is internally consistent.
x is anything at all
“point” is structureless point particles.

The rest of your post continues to miss the point.

Please note:
There can be no logical contradiction inherent in the concept of state without storage unless there is an axiom that prohibits it.

Logic is a system of reasoning which can be expressed formally. The only way something can be logically impossible is if a contradiction can be formally derived from the axioms of that system. There is no way to derive a contradiction from the basic axioms describing point particles (as illustrated by the computer simulation).

The fact that we use memory to perform these computations is irrelevant because memory is not part of the system we are computing. How don’t you understand this? I’m just as tired of repeating myself as you are. I’m not going to accept your logic on this point no matter how many times you repeat it because you’re refusing to address the argument.

All you’re doing is asserting that computer simulations don’t prove that point particles can exist, when I never said that they did. I assert that they are logically possible, which just means that no contradictions can be derived from that axiom.

Please note:
Nowhere do I claim that computer simulations prove that point particles are metaphysically possible, only logically possible

(and then I assert that metaphysical possibility is the same as logical possibility).

The fact that you refuse to understand the difference shows that disagreement 1 is still very much in force.

There can be no logical contradiction inherent in the concept of state without storage unless there is an axiom that prohibits it.

Prove it.

That’s my point.

You don’t get to just assert things. You have to prove them. In a way that doesn’t beg the question. Because it could well be that “the concept of state without storage” is self-contradictory (just as the concept of a disembodied mind might be self-contradictory, or the statement that a^n + b^n = c^n might be self-contradictory), without our currently knowing it (e.g. that last example took hundreds of years and a hundred pages of syllogisms to finally discover that it is, indeed, self-contradictory).

Again, I explain this problem in my post The God Impossible. You really need to read that again, because you seem to really not be getting it.

You are also still confusing logical with metaphysical possibility (by which here you seem to mean what I call physical possibility in a different but logically possible universe, although that is simply the same thing as saying it’s logically possible, full stop.).

But metaphysics is moot. I have consistently been talking about logical possibility. Only. And it is my original statement (of logical impossibility) that we have been talking about.

It breaks down like this:

(1) If x is only logically possible when y, then you cannot conclude that x is logically possible without y.

(2) If you do not know whether or not x is only logically possible when y, then you don’t know that x is logically possible without y.

This is not an “axiom.” It’s an undeniable fact of logic. The propositions stated above are necessarily true. Logically necessarily true. This is not a “metaphysical” question. Those propositions are true for all x and all y.

For example:

If multiplication is only logically possible when addition is possible, then you cannot conclude that multiplication is logically possible without addition. And if you do not know whether or not multiplication is only logically possible when addition is possible, then you don’t know that multiplication is logically possible without addition. (It’s not, BTW. Unless…transfinite numbers behave differenlty than finite numbers. Not an easy question there. Hence, our lack of knowledge does not justify asserting what we don’t know.)

Thus:

If a simulated thing is only logically possible when a simulator exists, then you cannot conclude that a simulated thing is logically possible without a simulator. And if you do not know whether or not a simulated thing is only logically possible when a simulator exists, then you don’t know that a simulated thing is logically possible without a simulator.

This is not a metaphysical statement. It’s a statement of logical necessity.

Thus the question becomes: are there some simulated things that can’t exist outside of simulators? You cannot magically know the answer to this from the armchair. If you cannot demonstrate that this is always false (“there some simulated things that can’t exist outside of simulators”), then you cannot claim it is always false. Yet that is what you are doing. But as just shown, you cannot claim to know such a statement is always false (because for many things, it is indeed true: reference “multiplication” and its dependency on “addition”). You have never demonstrated any reason to even believe it is always false, much less proven it is always false, in general (i.e. you have not proved either (1) or (2) false), nor in particular (i.e. you have not proved that (1) and (2) do not hold for simulated particles, nor even that structureless particles don’t satisfy the conditional in (1)).

If structureless particles can only be simulated using a structure to store the properties of those particles, then it certainly looks like this simulated thing is only logically possible when a simulator exists. This is not a metaphysical statement. It’s a statement of logical necessity. It follows necessarily from the logically necessary truth of (1) and (2). The notion of any simulated x without a structure to make the simulation possible looks self-contradictory. But that is not a formal proof, I agree. Just grounds for a strong suspicion. That’s why the issue is of justification, of warranted skepticism.

That we can only simulate x using structure might not mean that x can’t exist without structure in some logically possible universe. But neither can we conclude that x can exist without structure (in any logically possible universe)–when all we have ever seen, and all we can ever even imagine (without circular logic) is simulating x using structure.

Here, “simulation (x)” necessarily (logically necessarily) includes a structured computer. If it does not, then the argument is circular (you are assuming in A1 the existence of what you purport to conclude in A2). A circular argument is a fallacy. Fallacious arguments are not valid.

I know of a few theologians in my country that would point out that the basic physics required for the scenario you describe nonetheless requires a sort of “universal creative principle” or something like that, somewhat related to energy as a creative force… Which, as a side note, reminds me of the “solution” described by Dan Brown in his book “Angels and demons”, in which basically energy=God. (Do you happen to have read it and have found any weak point in it?)

I’m always puzzled by this kind of argument because all it seems to do is assign an unnecessary metaphysical label, when the “act of creation” examined is clearly constrained by basic physical laws. I find this to be completely subjective and arbitrary and anyway I think it would, at best, support a form of deism.

What are your thoughts? Do you think that your argument may allow the possibility of deism, or are there good reasons to reject that too?

Deism would not be required (since on the model here entailed, almost any random start would do, and most logically possible random starts are unintelligent; and an unintelligent cause is not a deity in any meaningful sense). As to whether it’s nevertheless possible, see my followup post: The God Impossible.

If universes can pop into existence, for lack of a law restricting it, why don’t we see random things popping into existence within the universe? Do you assume some platonic (abstract)restriction pops into existence along with the universe? But this would imply this law is as likely to disappear at any time, and other platonic laws could come and go. So this begs the question of why is there regularity and order to the universe?

IMO there has to be some order to existence, such that it is not the case that anything and everything can pop into and out of existence. Theists point to a God imposing this order (without accounting for the order that is inherent to God himself), but I think it also feasible that there is a material foundation of existence that constrains what can and cannot happen.

Fred said:If universes can pop into existence, for lack of a law restricting it, why don’t we see random things popping into existence within the universe?

Because in this universe rules exist that prevent that (such as the first law of thermodynamics). Of course, in actuality, random things do pop into existence within this universe (read up on virtual particles), but even that is governed by rules (quantum mechanics).

It is only when no rules exist that no rules exist to prevent any random thing from happening. Thus read P2 again. That’s the essential premise in the argument.

What is the ontology of the rules now governing this universe? Probably the geometry of interdimensionality, as suggested by Superstring Theory. Once a certain manifold of dimensions materialized at random, what could happen in that manifold is governed by the physical geometric facts of that manifold (thus limiting what sorts of particles can exist and how they would behave).

Richard – You seem to be assuming the universe could restrict what would otherwise be possible. I see a problem with this.

You apparently assume that the pure random landscape produced this superstring arena, and this arena can produce a universe such as ours. Within the context of the superstring arena, superstring nature would restrict what occurs within that arena.

However, the superstring arena itself is within the broader purely-random landscape. This means there nothing that restricts the evolution of this superstring arena. As the arena evolves from one state of affairs to the next, nothing restricts it – so we can expect purely random changes from one state affairs to the next. This is inconsistent with the regularity we observe in the universe.

I think there needs to some order, rather than pure randomness, in the fundamental basis of ontic reality (the landscape). Only then can there be orderly evolution as the fundamental landscape evolves.

Your logic doesn’t follow. The superstring landscape is restricted by the laws of geometry, which are necessarily true for all spaces. There is therefore no “broader, purely-random landscape,” unless there are non-spaces where things can exist (which we don’t reside at, so what happens in them is irrelevant to us) or spaces that produce from their geometry results not included by any superstring theory (in which case superstring theory is simply incomplete, but a more inclusive meta-theory would still obey the same fact of consistency because it, too, would be restricted by the laws of geometry governing all spaces).

In short, if all things are possible (except what is logically impossible), then at least two different things can come to be: (A) spaces with rules, and (B) spaces without rules; (B) is probably impossible (since to have no rules is to not obey the laws of geometry, but the laws of geometry govern all spaces) and even if possible, is clearly not where we find ourselves (in which case (B) spaces may exist, just not around here). Obviously, life (much less intelligent life) is only likely to arise in (A) spaces. Thus, of all the random spaces that come to exist, even if (B) spaces are possible, countless (A) spaces will still exist, even if there are also countless (B) spaces, and we will always only ever find ourselves in an (A) space.

I discuss some aspects of this in my follow-up post The God Impossible (where you can adapt the idea of Boltzmann worlds to the possibility of (B)-space civilizations is addressed, which are shown to be much less probable and thus much less frequent than the corollary to (A)-space civilizations).

The “broader, purely random landscape” to which I referred was the context you described as: “when nothing exists (except that which is logically necessary), then anything can happen (whose happening is logically possible).” The question is: what becomes of this metaphysical rule “anything can happen” when something DOES exist?

You had indicated that the minimum state of existence (i.e. the closest we can get to nothingness) includes all that is logically necessary. It follows that the metaphysical rule “anything can happen” is logically necessary, and this means it doesn’t go away just because something exists.

Now you say, “The superstring landscape is restricted by the laws of geometry, which are necessarily true for all spaces.” Geometry is necessarily true, and this certainly imposes some restrictions on the “anything that can happen,” but only with respect to that which follows solely from the geometry of the superstring construct. The superstring construct itself is still subject to the logically necessary “anything can happen.” Its geometry can’t be violated, but its geometry can change (say) from a cube to a pyramid because it is not logically impossible: it is not violating the rules of geometry and there is nothing that sustains its existence across states of affairs.

It follows that the metaphysical rule “anything can happen” is logically necessary, and this means it doesn’t go away just because something exists.

That’s a non sequitur. The metaphysical rule “anything can happen” is logically necessary only when nothing exists to prevent anything from happening. As soon as something exists that can stop something from happening, it is no longer the case that anything can happen. This was very clearly argued and explained in the original article.

As to whether nothing sustains the existence of a specific geometry, that is a question of fact, not logic. There might be universes where nothing prevents that universe from wobbling in and out of all sorts of shapes and topographies at random. But there will also, by inevitable random chance, be universes where the particular geometries prevent that (as any specific change cannot occur without other specific changes preceding it, the fundamental cause of a law of causation).

“The metaphysical rule “anything can happen” is logically necessary only when nothing exists to prevent anything from happening. As soon as something exists that can stop something from happening, it is no longer the case that anything can happen. This was very clearly argued and explained in the original article.”

Does the existence of anything somehow restrict other things from coming into existence? Or are you assuming that some universes just happen to have some random law that restricts what can exist? The former seems like a purely arbitrary assumption, so I’ll assume that’s not what you mean.

If it is a random natural law that creates the restriction, then what is it that keeps such a random law in existence within this universe? Anything that comes into existence by pure random chance could as easily cease existence by random chance at any time – including such a natural law. This is directly related to the second point.

“But there will also, by inevitable random chance, be universes where the particular geometries prevent that (as any specific change cannot occur without other specific changes preceding it, the fundamental cause of a law of causation).”

This doesn’t address my objection. If the geometry comes into existence by random chance, then it could cease to exist by random chance from one instant to the next. Let’s say our universe has experienced the random good fortune to continue existing for 13.7 billion years, enabling us to exist today. The odds are still quite low that this good luck will continue. Every instant that passes requires another lucky role of the dice, and since anything can happen, the odds against winning even a single roll are infinite, since there are infinitely many possibilities.

Does the existence of anything somehow restrict other things from coming into existence?

No. Only the existence of things that restrict other things from coming into existence, restrict other things from coming into existence. Obviously.

If it is a random natural law that creates the restriction, then what is it that keeps such a random law in existence within this universe?

Its innate properties. What you are talking about in fact is called a modal property. On which see Sense and Goodness without God III.5.4.3, pp. 128-30.

Something can have the property of having no modal properties, i.e. it can have the property of just continuing to exist randomly, and such a thing can dissolve randomly. But it can also have the property of remaining forever what it is until something causes it to change.

Causation is just geometry extended into the dimension of time.

That leaves the question of which universe we are in, one that just hangs together randomly and could dissolve at any minute, or one whose geometry is intrinsically modal. Probabilities decide strongly in favor of the latter, as I explain in The God Impossible.

1. If nothingness has spawned an actually infinite number of universes, then an argument can be made against the existence of an actually infinite number of things which undercuts your theory.

2. If nothingness has spawned infinitely many universes, then there is nothing preventing universes with different properties that our own from appearing within our universe (universes come into being from nothing, not ‘in nothing’ as if nothing was ‘something’ existing outside the universe). Yet we do not observe mini-universes forming within our universe.

I’m not sure what you mean. Do you mean there is an argument against the existence of an actually infinite number of things? That’s simply not true, so it’s a moot point. All mathematicians will tell you that there is no logical impossibility in an actual infinity. In fact, the entire mathematical system of calculus works precisely because that premise is false. That you heard differently from Christian apologists doesn’t change the fact. They are scamming you.

Even so, if it were true, then the argument would simply be adjusted, since in the absence of all governing properties, all logical possibilities can occur, so if an actual infinite is logically impossible, it is excluded, which means the argument must replace that with the highest logically possible number of universes (and when you do that, you get essentially the same result: only, instead of an actual infinite number of universes, you get a ridiculously umteen zillion gazillion universes).

However, you might notice that it is logically impossible for there to be a number than which no greater number can be, which suggests the premise that an actual infinity is impossible is itself false (since the impossibility of an actual infinite entails there is a number of universes than which no greater number can be, but it is the latter that is impossible).

As for 2:

That’s false. The only way universes can spontaneously appear is if nothing exists to prevent it–that crucial premise, P2. Once you remove P2, your conclusion no longer follows. And when a universe exists, P2 does not obtain within it. Our universe’s matter-energy, space-time, and physical laws now limit what can happen within this universe.

I should also mention that you are also wrong to assume your own premise has been falsified.

On standard chaotic inflation theory, the most popular theory that most actual cosmological scientists suspect is correct, other universes are forming inside ours–but at distances of perhaps trillions of lightyears (do to the extreme low probability of that occurring, the frequency per parsec is extremely low, resulting in seeing only one every few trillion lightyears or every few hundred billion lightyears, or whatever it works out to). Our visible horizon extends to only 14 billion lightyears. We can’t see the vast majority of our own universe.

Likewise, on Smolin selection theory, every black hole has generated a new universe within our universe (and thus universe generation is so common we can even see the access points to billions of them), it’s just that those universes are on the other side of black holes (tightly constrained spaces that no light can get through, thus we can’t see what’s over there).

And so on.

Thus, there are many ways that our universe could indeed be generating new universes (in accordance with its actual, realized structure and thus its actual, realized physical laws, not in accord with P2, which no longer obtains here), without our being able to verify it. We therefore can’t falsify it either. Which does not permit the conclusion (yet) that it is happening; but it forbids the conclusion (so far) that it is not.

I haven’t had a chance to read all that others have posted here, so my point may already have been covered. However, it seems to me that the very core of your argument is based on a fallacy: namely, the idea that ex nihilo nihil fit is meant as a law restricting what “nothingness” can do. That is incorrect. It is instead an extrapolation from the nature and definition of “nothing” (very much like your own extrapolation of “absolute nothing”) leading to the recognition that any potentiality, creative power, etc would not be present. It is not enough to have no restrictions; creation requires something with power and potential. Nothing is holding me back from bench-pressing 600lbs, except a lack of power to do so, and therefore from the full description of me it follows that I cannot lift 600lbs. This is not a law, nor a reference to logical impossibility, it is just an observation about what it means to be me. Note: Your reasoning is actually self-defeating, in light of this analysis, since saying “nothingness cannot be restricted” is the same kind of statement as “nothingness has no powers to create anything”; not a law, just an extrapolation from what it means to be “nothing”. These are just analyses of what “nothingness” entails, and if you can do it, so can those who say ex nihilo nihil fit.

Besides, if your reasoning actually held, we would have to abandon science, induction, and any discourse about probability or likelihood, since we might just be in one of the infinite number of Universes where I happen to flip heads 1,000 times, inexplicably (for a simplistic example). I reference Robin Collins’ comments on the “unrestricted multiverse” in his chapter of the Blackwell Companion to Natural Theology. Really all events have equal probability if we are just one Universe in an infinite multiverse.

Then we can analyze your argument and see if it holds up. If it does, then it will be an adequate refutation.

But be careful. Because as soon as you say something lacks all abilities, you are also saying it lacks the ability to stay the same (i.e. it then lacks all modal properties as well). Which then entails P2.

I do not see any way for you to get the conclusion you want, from the premise you intend. Which was the whole point of my article.

Besides, if your reasoning actually held, we would have to abandon science, induction, and any discourse about probability or likelihood, since we might just be in one of the infinite number of Universes where I happen to flip heads 1,000 times, inexplicably (for a simplistic example).

That’s false. It would be extremely unlikely that we would be in that universe. So the possibility of it is irrelevant to inductive logic (just as all Cartesian Demons are). I discussed this in my follow-up post about Boltzmann universes in The God Impossible. You can read up and discuss that issue there.

Fred:If it is a random natural law that creates the restriction, then what is it that keeps such a random law in existence within this universe?

Richard: Its innate properties. What you are talking about in fact is called a modal property. On which see Sense and Goodness without God III.5.4.3, pp. 128-30.

Something can have the property of having no modal properties, i.e. it can have the property of just continuing to exist randomly, and such a thing can dissolve randomly. But it can also have the property of remaining forever what it is until something causes it to change.

I looked at your book and saw that you defined model properties as “causal consequences of matter-energy in space-time.” This describes only a restriction on what is physically possible, but you had indicated that everything that is logically possible could and would happen. It is logically possible for a natural law or material object to disappear.

It is for this reason that I think it more rational to assume there is a material basis for reality, with inviolable natural law. The Many Worlds Interpretation of Quantum Field Theory provides a potentially infinite landscape of worlds, with varying localized laws of physics. Fundamental natural law would be common to the entire landscape, providing physical constraints on what can occur. The localized laws are special cases of these fundamental laws with wide degrees of freedom, wide enough to give you all the possibilities you need – but with a stronger warrant for assuming modal properties that can restrict what can occur because they are based on inviolable fundamental natural law.

I looked at your book and saw that you defined model properties as “causal consequences of matter-energy in space-time.”

That’s the ontology of modal properties in a naturalist universe. Not the definition of what a modal property is. I define modal property on p. 128, without reference to its ontology; then I ask how modal properties can exist on naturalism; then I answer that by providing a naturalist ontology of modal properties on pp. 129-30.

Here in this article I am asking about one level beyond naturalism: I’m asking what would happen if no ontology existed, except that of absolutely nothing.

So, yes, in this universe, there is a material basis for reality, with inviolable natural law. Because that’s one of the things that popped out of the nothing, and the only kind of such things that we would ever find ourselves in. If reality began in a state of nothing. Note that I do not affirm that to be the case. I allow it may well be the case that there has always been something, and never been nothing. In which case there could well have always have been “a material basis for reality, with inviolable natural law”; but in that case, the cosmological argument for God fails (as there is nothing for a God to have begun).

However, there is a problem with positing “inviolable natural law” with no ontology. What makes it inviolable? Something must exist that does so. So what is that something? I propose it is space-time itself (and the logical impossibility of incoherent geometries). That’s as good a theory as any right now. In the meantime, theoretical physicists are working the problem.

However, there is a problem with positing “inviolable natural law” with no ontology. What makes it inviolable? Something must exist that does so. So what is that something? I propose it is space-time itself (and the logical impossibility of incoherent geometries). That’s as good a theory as any right now. In the meantime, theoretical physicists are working the problem.

The ontological basis of everything would be the Universal Wave Function.
In the hypothesis, everything in existence is part of the wave function. It is the sine qua non of material reality. Particles are disturbances in the wave; virtual particles are transient disturbances. It even subsumes natural law – behavior is due to the characteristics of the wave function. It eliminates the need for Platonic law, which your model seems to assume exists (what grounds platonic law? Some theists claim it is only grounded in the mind of God).
Wikipedia has a decent article on the Many Worlds Interpretation.

A wave function is just geometry. My theory requires no Platonic anything, just space-time. Just like yours. There are infinitely many wave functions, producing infinitely many universes. One of them is ours. My argument follows therefrom.

With regards to my first objection, where you see malevolence and deceit (“scamming”), I see reasoned arguments:http://plato.stanford.edu/entries/cosmological-argument/#4.2 Nevertheless, I think we can successfully plug “potential infinities” (there is no logical contradiction that I know of involved in a potential infinite number of things) into your argument, rather than actual infinities. So, I will retract my first objection.

Focusing on my second objection, can you prove that the universe’s matter-energy, space-time, and physical laws prevent {another universe with different properties from forming within this universe without any causal conditions whatsoever} (and I’m not talking about universes forming within our universe via necessary or necessary and sufficient causation, as predicted in the models that you referred to)? It seems to me that you cannot.

If you deny the principle that whatever begins to exist has a cause, then, at best, what you can prove is that whatever begins to exist in a universe and is bound by the properties of that universe has a cause. Since another universe with different properties is not bound by the properties of our universe, another universe can come into being within our universe without any causal conditions – again if we accept that things can come into being without any causal conditions whatsoever(and, by the way, virtual particles have necessary – though not sufficient – causal conditions).

Therefore, your argument (specifically, premise 2), unless you can prove otherwise, implies that our universe can spawn, within itself, without any causal conditions whatsoever, an incalculable number of universes, some of which will be stable and observable. Since we do not observe such stable universes within our universe, in spite of our advanced detection technology, it follows that your argument is strictly invalid.

First, things can come into existence without causation even in our universe–everything, every universe even, has a quantum mechanical probability–it’s just that universes are incredibly improbable. We won’t see them they are so rare. So your falsification conditions don’t apply. I discuss this, again as I said, in my post on The God Impossible.

Second, my argument only follows if P2 is true. Locally (where we are now), P2 isn’t true. So nothing can follow from my argument for the local region of spacetime we are in. For example, you cannot walk into a fourth dimension of space, because there is none here. The universe that “popped” into existence only had three open spatial dimensions. That prevents four-dimensional objects from existing (other than in the extension of time).

So could a fourth dimension of space suddenly appear somewhere? Maybe. But because it hasn’t happened in billions of years, obviously something is either preventing it or rendering it extremely improbable. Therefore this universe has a property (a modal property) that is doing that. It does not “necessarily” have that property, it just contingently does. Some other universe may lack it and thus change its dimensionality all the time. But such a chaos would be too unstable to produce observers, so we won’t find ourselves in one.

You are basically saying “if new dimensions could open up, why don’t we see that happen?” To which there can be three answers: it’s logically impossible, it’s impossible because this universe has a physical property that prevents it, or it’s extremely improbable because this universe has a physical property that makes it so (or because it is logically necessary, for some reason as yet unknown to us).

We cannot decide between those possible hypotheses on present observations.

That confuses “concepts” with what concepts are concepts of. You do not need a concept of nothing to have nothing, any more than you need a concept of an empty box to have an empty box. So that argument doesn’t address what I am talking about at all.

At most one can say that because we can now think about whether there was nothing (before there were minds to think about it), then obviously something now exists (and so we cannot say that “there is, at the present time, absolutely nothing”), and therefore, if there was nothing, somehow it became or was replaced with something. But there are many different ways that could have happened. My argument discusses one of them.

That author also is unaware of how Aristotelian physicalism answers Platonism and thus resolves ontology in favor of materialism, not constructivism. I discuss this specifically and in detail in Sense and Goodness without God and in my response to Michael Rea’s attempt at a similar argument. I have also addressed the physicalist ontology of mathematics, for example, in several places (for a start, see my old blog posts).

[P.S. In case it isn’t obvious, “the ability to be thought” is not a property “nothing” has; until there is something that can think. Thus, the author is confusing intrinsic with relational properties. The ability to think something is the property of a thinker, not the thing thought. Insofar as a thing shares in the property of being thinkable, it is only relative to a thinker; change the properties of a thinker, and you change what is and isn’t thinkable, but the things themselves don’t change at all–so clearly, this is not really a property of the things being thought about. Except potentially. But that then gets us back into the distinction between actual and potential properties.]

Dr. Carrier, your position seems to be that (a) it is possible for a universe to come into being from nothing, without any causal conditions whatsoever, and (b) it is impossible for a universe to come into being in a universe, without any causal conditions whatsoever (for example, without a quantum mechanical probability). But the idea that “a universe can come into being from nothing” simply means that “a universe can come into being without any causal conditions whatsoever”. So, if you affirm that “a universe can come into being from nothing”, then you must accept that it is entirely possible for a universe to come into being from nothing within a preexisting universe, that is, come into being within a preexisting universe without any causal conditions whatsoever. Therefore, on your theory that it is possible for universes to come into being from nothing, it is utterly mysterious why we don’t observe universes coming into being from nothing within our own universe. You theory is therefore explanatorily deficient. For that reason, we should prefer the principle that everything that begins to exist has some causal conditions for its existence.

My argument shows that (a) is true only if P1 is true. Wherever P1 is not true, then (a) does not obtain (unless there is some other route to (a)).

Unless by (a) you include quantum mechanical causation (which is not the absence but the presence of a causal system, in particular lawful virtual particle formation), in which case yes, universes can pop into existence just as we’ve proven photons can, it’s just that the probability is so immensely low we can never expect to see it happen (unlike spontaneous photon formation, which is vastly more probable, and thus we can observe it, at least indirectly, e.g. the casimir effect). But by stating (b) I assume you mean by (a) even the absence of quantum mechanical systems.

Apart from that, the reason (b) holds is that (a) holds only if P1; and locally, P1 does not hold (as we can directly observe). Whether (a) can obtain without P1 is not something my argument shows; if you, however, have an argument for it, feel free to produce it–but it won’t derive from my argument, as mine only follows from P1.

Thus, you are simply not getting this point. I am not saying “a universe can come into being from nothing”, I am saying “a universe can come into being from P1”, which means we will only observe that happening wherever we observe P1. Which is not anywhere around here. Therefore my argument does not entail what you suggest. At all.

The problem with your argument is that the principle “if nothing exists (apart from logical necessity) to prevent anything from happening or to make any one thing happening more likely than any other thing, then universes can come into being without any causal conditions whatsoever (including without QM causal conditions)” seems intuitively true not only for universes coming into being not within universes, but also for universes coming into being within universes. See the argument below:

1. If nothing exists (apart from logical necessity) to prevent {a universe without causal conditions (including no QM causal conditions)} (hereinafter ‘p-universe’) from coming into being or to make {a p-universe not coming into being} more likely than {a p-universe coming into being}, then a p-universe can come into being.

2. Within our universe, nothing exists (apart from logical necessity) to prevent {a universe without causal conditions (including no QM causal conditions)} (hereinafter ‘p-universe’) from coming into being or to make {a p-universe not coming into being} more likely than {a p-universe coming into being}.

Once we apply the principle within our universe, the principle turns out to be explanatorily deficient (in terms of explaining why we do not observe universes coming into being within our universe without any causal conditions whatsoever, including without QM causal conditions). Since the intuitive principle that whatever begins to exist has causal conditions for its existence is not explanatorily deficient, it is more plausibly true than your principle. Therefore, your argument is plausibly unsound.

(2) is false. There are QM and spatio-temporal causal conditions that limit what happens within this universe. For example, a universe popping into existence within this universe is governed, as I’ve repeatedly said, by a definable QM probability (which, though not zero, is extremely small), which follows from the physical properties of space-time (the probability of a given space-time region spontaneously expanding, as is logically required to generate a new universe, is governed by the physical properties of space-time in this universe; and the existence of those properties entails the local falsity of P1).

(3) is also moot. Because it can be true, and still have (4) be false, where (4) is your premise that “we do not observe universes coming into being within our universe without any causal conditions whatsoever.” Since (4) and (3) are compatible (both can be true), your conclusion that we can reject your own assumption (1) because of our observation (4) is invalid. You have to calculate the probability of a p-universe coming into being, per cubic parsec or something, first; only then can we determine if we should have observed it by now or not.

And of course, as soon as you start asking what that probability “per cubic parsec” is, you will start to realize why (2) is locally false. It can only be true in the absence of a universe with causal properties. Hence, it is only true when P1 is true. And P1 is not locally true. Whether it was ever true is not a question I attempted to answer.

Finally, your premise, I shall number it (5), that “whatever begins to exist has causal conditions for its existence is not explanatorily deficient” is either false or moot, depending on how you define “causal conditions.”

On a broad definition of “causal conditions,” P1 is a causal condition; therefore (5) is compatible with P1 and therefore cannot be used to argue against P1. Thus, I can just as easily use (5) to bolster P1 (and in fact I effectively give such an argument in this article). You therefore cannot use (5) as an argument against P1. I’ve made this point several times already.

On a narrower definition of “causal conditions,” (5) entails something has always existed and therefore there has never been a beginning. This is because the causal conditions would also have to begin to exist–since as soon as they exist their effect occurs, therefore they cannot have existed for any significant amount of time prior to their causing the effect. So either those causal conditions began to exist without a cause (in which case (5) is false), or all causal conditions have in turn causal conditions, entailing an infinite regress of causal conditions, which entails nothing began to exist, but rather there has always been something, and has never been nothing. Which I point out in my article is entirely possible, but refutes cosmological creationism (unless you can validly prove that that endless chain of causal conditions must necessarily include a god in it somewhere, but no such argument exists, and at any rate, we are then no longer arguing creation ex nihilo).

Dr. Carrier, unless you can prove that, in some possible world, it is logically necessary that the spontaneous expansion of a space-time region in our universe is governed by a QM probability (which is not obviously or intuitively true), my argument stands:

1. If nothing exists (apart from logical necessity) to prevent a universe without causal conditions* (‘p-universe’) from coming into being or to make {a p-universe not coming into being} more likely than {a p-universe coming into being}, then a p-universe can come into being.

2. Within our universe, nothing exists to prevent a p-universe from coming into being or to make {a p-universe not coming into being} more likely than {a p-universe coming into being}.

Dr. Carrier, unless you can prove that, in some possible world, it is logically necessary that the spontaneous expansion of a space-time region in our universe is governed by a QM probability (which is not obviously or intuitively true), my argument stands…

Incorrect. It doesn’t have to be logically necessary. It is enough that it is a contingent fact of a given universe. It need not be true in all universes. We went over this before. As soon as a limiting property exists, P1 is no longer true, and therefore P2 is no longer true, and therefore your (2) is no longer true.

And the fact that “the spontaneous expansion of a space-time region in our universe is governed by a QM probability” is a contingently true property of this universe is empirically confirmed. So it’s not in dispute.

This is also why your (3) and (4) do not contradict each other, as I explained. Thus, (4) being true does not refute (3). Which is why your new (5) does not follow even from your own premises (a fact you still fail to acknowledge).

But this is also why your (2) is false: we do not live in a universe where “nothing exists” to prevent spontaneous expansions. We live in a universe where something exists to prevent them (the QM properties of local spacetime). Where did that “something” come from? My argument answers that question. In no way is that “something” a logical necessity. Although it would be interesting if it were, and Victor Stenger does argue that it is, it’s being so is not necessary for my argument, which only requires that this “something” be logically possible, not that it be logically necessary. Once it exists, it exists. But perhaps not every universe will necessarily have it. We’ll just only ever find ourselves in one that does.

You also are not adequately addressing my other points.

First, you are attempting verbal legerdemain with the words “something” and “condition.” You say “a causal condition is something that is involved in the causation of something else (‘nothing’ is not something),” but your parenthesis is a verbal game, an equivocation fallacy as regards what the meaning of “condition” and “something” are. If P1-nothing has causal properties (as it necessarily does, per my argument), then it is a “causal condition.” To maintain that a “causal condition” has to be “something” more, you would have to prove that only something more substantial than P1 can ever cause anything to happen, which means you would have to show my syllogism to be logically invalid (i.e. you have to grant all its premises, and then prove the conclusion still has to be false, identifying a fallacy somewhere). Because otherwise my syllogism refutes your inference that a “causal condition” has to be “something” more substantial than P1.

Second, Craig’s theology is not even explanatorily intelligible, much less adequate. He wants a God to exist and make decisions when no time exists in which to make them and no place exists in which to exist at all (the argument from nonlocation also applies to time, becoming also an argument of nonlocation in time). That’s unintelligible. The only way around this is to bite the bullet and admit that God necessarily exists in time and space (he exists “now,” thus he has a location in time, and he exists “here,” in some sense, i.e. as opposed to not existing anywhere or not existing in this universe but in some other place; God is usually understood as omnipresent, so he would have location in space: he is everywhere), but then God “began to exist.” Because God’s existence begins with the existence of time, just like all the universes do that my argument entails follow from an initial state of nothing.

In short, there cannot be a God at a location of “never” and “nowhere” (a location at no time and in no place).

If God “began to exist” then he needs an explanation of his existence, and that explanation must have begun to exist, and so on, turtles all the way down. Unless not everything that begins needs a cause or explanation of its existence. Pick one or the other. There is no third option. In the P1 scenario, God is exactly analogous to the potentiality of the nothing-state (both necessarily have causal powers, and neither of them “began to exist” any more or less than the other: i.e. any argument that God did not begin to exist, will entail P1 did not begin to exist either). Except there is one difference: the potentiality of the nothing-state is vastly simpler than God, and thus Ockham’s Razor slashes God out of the picture. If P1 explains all observations (and it does), then adding God to P1 is adding unnecessary theoretical elements (a causeless mind, with an amazing addition of properties and powers, including infinite quantities of thoughts and abilities). It is therefore unnecessary.

(And indeed, P1 explains all observations even better than God theory does–see my chapter on this in The End of Christianity. God theory is actually an extremely inadequate explanation of what we observe to be the case, as I document extensively there; the more so if we are talking about a Christian God, as I demonstrate in Why I Am Not a Christian.)

I see no relevance to the question. Whether married bachelors can exist depends on how you define the words, which makes this a matter of semantics. And semantics has nothing to do with metaphysics.

As for the metaphysics, if x has the potential to exist and the potential to not exist, the potential for x to both exist and not exist at the same time does not exist. Unless you want to argue the contrary. But that’s on you.

We call this the LNC, but that’s really just a declaration that “distinctions exist” (since the only way the LNC could be false is if there are no distinctions, i.e. no difference between x existing or not existing), which is a statement of fact. One that we can confirm directly in basic empirical observation (cognito ergo sum) and in conceptual modeling (since any argument about possible outcomes must incorporate the property of distinctions existing or not existing; and models only produce results when they incorporate the property of distinctions existing, so we usually only consider those possibilities–they’re the only ones that are interesting–while other worlds simply won’t have anything in them, in the sense of anything distinguishable from anything else, so we can disregard them).

Unless you can prove* that, in some possible world, the spontaneous expansion of a space-time region in our universe is always governed by a QM probability (which is not obviously or intuitively true), my argument stands:

1. If nothing exists (apart from logical necessity) to prevent a universe without ‘p-causal-conditions’** (‘p-universe’) from coming into being or to make {a p-universe not coming into being} more likely than {a p-universe coming into being}, then a p-universe can come into being.

2. Within our universe, nothing exists to prevent a p-universe from coming into being or to make {a p-universe not coming into being} more likely than {a p-universe coming into being}.

Unless you can prove* that, in some possible world, the spontaneous expansion of a space-time region in our universe is always governed by a QM probability (which is not obviously or intuitively true), my argument stands:

No, it doesn’t. I don’t know what kind of logic you think you are using, but this simply doesn’t follow. The burden is on you to demonstrate that something is possible in this universe. It is not on me to prove a negative. Observations confirm my conclusion. They do not confirm yours. Therefore your premise that a non-QM-governed spacetime exists (much less exists locally) is no different from the premise that Leprechauns exist locally. Indeed, it’s worse, since it’s more analogous to saying that gravity doesn’t exist, in the face of vast empirical evidence that gravity exists. Because you are saying spacetime is not governed by QM, in the face of vast scientific evidence that spacetime is governed by QM.

Thus, your premise (2) is simply false: empirically, scientifically false. Just as it would be false to say “Within our universe, nothing exists to prevent apples from falling up.”

(You still also fail to show how (4) entails (5)…there is no connecting premise; yet whether (4) entails (5) will depend on the frequency with which p-universes will come into being if (2) were even true [which it’s not, but even supposing it were], and you have done nothing to show that that frequency would be high enough for us to observe even one instance.)

(Premise (7) is also still false: (a) if “causal conditions” is allowed to mean any state that can cause another state, then (1) describes a state that can cause another state, as my argument demonstrates, but indeed as even your own wording of (1) entails, and therefore (1) is a “causal condition” and therefore it is not the case that “Every universe that begins to exist has causal conditions for its existence” is true if and only if (1) is false; and (b) if “causal conditions” is restricted to exclude logically possible causes, then “Every universe that begins to exist has causal conditions for its existence” is itself false, since there are some possible universes that can begin to exist from causes other than “causal conditions” as you are then defining them–again, as my P1 argument proves.)

Dr. Carrier, I have again reformulated my argument to address your objections:

1. If nothing exists (apart from logical necessity) to prevent a ‘p-universe’* from coming into being or to make {a p-universe not coming into being} more likely than {a p-universe coming into being}, then a p-universe can come into being.

2. Necessarily, the spontaneous expansion of any space-time region in our universe (which is logically required when a universe is generated within our universe) is not always governed by a QM probability.

3. If (2) is true, then, within our universe, nothing exists to prevent a p-universe from coming into being or to make {a p-universe not coming into being} more likely than {a p-universe coming into being}.

4. Within our universe, nothing exists to prevent a p-universe from coming into being or to make {a p-universe not coming into being} more likely than {a p-universe coming into being}. [from (2) and (3)]

5. Within our universe, a p-universe can come into being. [from (1) and (4)]

6. We do not observe p-universes coming into being within our universe.

7. If (5) and (6) are true, then (1) is explanatorily deficient. [We can take any neighboring region of space-time and ask “why haven’t we detected a rapidly expanding p-universe there?” There’s no answer. It’s inexplicable. Therefore, (1) is explanatorily deficient.]

8. (1) is explanatorily deficient. [from (5) to (7)]

9. “Every universe that begins to exist has something that causes it to exist” is true if and only if (1) is false.

10. “Every universe that begins to exist has something that causes it to exist” is explanatorily adequate.

11. A principle which is explanatorily adequate should be preferred over a principle which is explanatorily deficient.

12. The principle “every universe that begins to exist has something that causes it to exist” should be preferred over (1). [from (8) to (11)]

13. The statement “if there was absolutely nothing in the beginning, then ‘p-universes’ exist**” is true if and only if (1) is true.

14. The statement “if there was absolutely nothing in the beginning, then ‘p-universes’ exist” is false. [from (12) and (13)]

Now, if (14) is false, then the only premises which are plausibly false are (1) and (2). Since you are committed to (1) and (14), you must prove that (2) is false.

* By ‘p-universe’, I mean a universe without any ‘p-causal-conditions’, where ‘p-causal-conditions’ are defined as things which are involved in the causation of other things.

2. Necessarily, the spontaneous expansion of any space-time region in our universe (which is logically required when a universe is generated within our universe) is not always governed by a QM probability.

What’s the frequency with which the spontaneous expansion of any space-time region in our universe is not governed by a QM probability?

Dr. Carrier, I have once again reformulated my argument to address your objection:

1. Necessarily, the spontaneous expansion of any space-time region in our universe (which is logically required when a universe is generated within our universe) is not always governed by a QM probability.

2. If (1) is true, then, within our universe, nothing exists to prevent a ‘p-universe’* from coming into being or to make {a p-universe not coming into being} more likely than {a p-universe coming into being}.

3. Within our universe, nothing exists to prevent a p-universe from coming into being or to make {a p-universe not coming into being} more likely than {a p-universe coming into being}. [from (1) and (2)]

4. If nothing exists to prevent a p-universe from coming into being or to make {a p-universe not coming into being} more likely than {a p-universe coming into being}, then, of all the logically possible things that can happen, {no p-universes coming into being} is one thing, one p-universe coming into being is another thing, two p-universes coming into being is yet another thing, and so on all the way to infinitely many p-universes coming into being, and likewise for every cardinality of infinity, and every configuration of p-universes.**

5. Within our universe, {no p-universes coming into being} is no more likely than one p-universe coming into being, which is no more likely than two p-universes coming into being, which is no more likely than infinitely many p-universes coming into being, which is no more likely than any other particular number or cardinality of p-universes coming into being. [from (3) and (4)]**

6. If each outcome (0 p-universes, 1 p-universe, 2 p-universes, etc. all the way to aleph-0 p-universes, aleph-1 p-universes, etc. [note that there is more than one infinity in this sequence]) is no more likely than the next, then the probability of any finite number of p-universes (including zero p-universes) or less having come into being is infinitely close to zero, and the probability of some infinite number of universes having come into being is infinitely close to one hundred percent.**

7. Within our universe, the probability of some infinite number of p-universes having come into being is infinitely close to one hundred percent. [from (5) and (6)]**

8. We do not observe p-universes within our universe.

9. If (7) and (8) are true, then (4) is explanatorily deficient.***

10. (4) is explanatorily deficient. [from (8) and (9)]

11. “Every universe that begins to exist has something that causes it to exist” is true if and only if (4) is false.

12. “Every universe that begins to exist has something that causes it to exist” is explanatorily adequate.

13. A principle that is explanatorily adequate should be preferred over a principle that is explanatorily deficient.

14. The principle “every universe that begins to exist has something that causes it to exist” should be preferred over (4). [from (10) to (13)]

15. The statement “if there was absolutely nothing in the beginning, then ‘p-universes’ exist” is true if and only if (4) is true.

16. The statement “if there was absolutely nothing in the beginning, then ‘p-universes’ exist” is false. [from (14) and (15)]

Now, if (16) is false, then the only premises which are plausibly false are (1) and (4). Since you are committed to (4) and (16), you must prove that (1) is false.

* By ‘p-universe’, I mean a universe without any ‘p-causal-conditions’, where ‘p-causal-conditions’ are defined as things which are involved in the causation of other things.

*** We can take any neighboring region of space-time and ask “why haven’t we detected a rapidly expanding p-universe there?” There’s no answer. It’s inexplicable. Therefore, (5) is explanatorily deficient.

1. Necessarily, the spontaneous expansion of any space-time region in our universe (which is logically required when a universe is generated within our universe) is not always governed by a QM probability.

You have no evidence supporting this premise. Let’s see the logical syllogism establishing this as a logical necessity. Until then, you are begging the question.

The parenthesis does not produce a logically valid argument–since “the spontaneous expansion of any space-time region in our universe” can be generated by QM and since that would generate a universe, this new (1) is actually necessarily false, i.e. it cannot be logically necessary; it could still be “possible” but that gets you stuck back with the prior versions of your argument which stumble at their premise (2).

Worse, your new premise (2) does not follow from your new (1) as stated. I assume you mean (2) to say “sometimes” nothing prevents universe creation (since clearly, even your new (1) entails most times QM does prevent it).

Thus, again, even if somehow you could establish (1), and you haven’t, you still have to prove that (1) entails the frequency of universe creation is high enough that we should expect to have seen one by now.

In attempting to do that, you seem to confuse overall frequency with observation frequency, which is a mathematical mistake. For example, our universe might generate one creation event every trillion years, and still generate infinitely many events. Thus (7) still does not entail (8) and therefore you still don’t get (9). Likewise, according to your own (4), our universe will generate infinitely many universe in each creation event, and thus could have only one spontaneous event ever, and still satisfy (7); and that event again might happen trillions of years from now, or it may have happened trillions of lightyears from us (and thus we won’t have seen it even if it already happened).

That’s why frequency of observation has to be calculated. But you have no way of doing that, and thus no argument to make. And that’s even granting your new (1), which we just saw is logically false; and when changed to an empirical premise is unevidenced.

Note that your own new (1) entails (4) only happens rarely, thus only rarely will there be an explosion of a random number of universes. Thus, you have to establish that it is not so rarely that we wouldn’t have seen one by now.

Then, of course, there is the added problem that we might in fact have seen them and just not realized it–if Smolin is correct and such creation events occur within every black hole; or if creation events continually occur at scales below our resolution (e.g. if every subatomic particle contains a creation event of universes that, scaled to us, are unobservable, but are, within their own frame of reference, as vast as ours–for instance our own universe could be within the electron of someone else’s universe).

In short, you have to get from (7) to (8), and you have provided no logical syllogism that does that. And it seems impossible, given all the possibilities you have to eliminate or account for.

And that’s even supposing you can prove (1), which you haven’t, and as it is a logical impossibility, you can’t. Modifying (1) back to something logically possible turns it into an empirical assertion, and then you have to prove (2), which you know you can’t do (that’s why you keep trying to avoid it by tinkering with your syllogism rather than dealing with the real problem: evidence).

1. The principle that “every universe that begins to exist has something that causes it to exist” is false.

2. If (1) is true, then, within our universe, space-time does not prevent a p-universe from coming into being (i.e. it does not prevent {an expanding universe which would become at least as large as a planet, within our frame of reference} from {coming into being without something causing it to come into being}), nor does it make {a p-universe not coming into being} more likely than {a p-universe coming into being}.*

3. Within our universe, space-time does not prevent a p-universe from coming into being, nor does it make {a p-universe not coming into being} more likely than {a p-universe coming into being}. [from (1) & (2)]

4. If (3) is true, then, within our universe, nothing exists to prevent a p-universe from coming into being or to make {a p-universe not coming into being} more likely than {a p-universe coming into being}.

5. Within our universe, nothing exists to prevent a p-universe from coming into being or to make {a p-universe not coming into being} more likely than {a p-universe coming into being}. [from (3) & (4)]

6. If nothing exists to prevent a p-universe from coming into being or to make {a p-universe not coming into being} more likely than {a p-universe coming into being}, then, of all the logically possible things that can happen, {no p-universes coming into being} is one thing, one p-universe coming into being is another thing, two p-universes coming into being is yet another thing, and so on all the way to infinitely many p-universes coming into being, and likewise for every cardinality of infinity, and every configuration of p-universes.**

7. Within our universe, {no p-universes coming into being} is no more likely than one p-universe coming into being, which is no more likely than two p-universes coming into being, which is no more likely than infinitely many p-universes coming into being, which is no more likely than any other particular number or cardinality of p-universes coming into being. [from (5) & (6)]**

8. If each outcome (0 p-universes, 1 p-universe, 2 p-universes, etc. all the way to aleph-0 p-universes, aleph-1 p-universes, etc. [note that there is more than one infinity in this sequence]) is no more likely than the next, then the probability of any finite number of p-universes (including zero p-universes) or less having come into being is infinitely close to zero, and the probability of some infinite number of p-universes having come into being is infinitely close to one hundred percent.**

9. Within our universe, the probability of some infinite number of p-universes having come into being is infinitely close to one hundred percent. [from (7) & (8)]**

10. We (as human beings) exist and we have not observed any p-universes within our universe.

11. If (10) is true, then (9) is false.

12. (10) is true.

13. (9) is false. [from (11) & (12)]

14. If “(1) is true if and only if (6) is true” is true, then “if (9) is false, then (1) to (7) are false” is true.

15. (1) is true if and only if (6) is true.

16. If (9) is false, then (1) to (7) are false. [from (14) & (15)]

17. (1) to (7) are false. [from (13) & (16)]

18. “If there was absolutely nothing in the beginning, then p-universes exist” is true if and only if (6) is true.

19. “If there was absolutely nothing in the beginning, then p-universes exist” is false. [from (17) & (18)]

* By ‘p-universe’, I mean an expanding universe which would become at least as large as a planet, within our frame of refe